A water station table at a marathon starts with 200 plastic cups on it. Every minute, 15 cups are taken from the table. How many minutes could have passed if there are fewer than 50 cups on the table?
Answers
So, the answer is 11 minutes or more. If exactly 11 minutes have passed,
To determine how many minutes could have passed if there are fewer than 50 cups on the table, we can set up an equation.
Let's denote the number of minutes that have passed as "m". At the start, there are 200 cups on the table. Every minute, 15 cups are taken from the table. So, after m minutes, the number of cups remaining on the table can be represented by the equation:
200 - 15m < 50
To solve for "m", we can isolate the variable by performing the following steps:
200 - 15m < 50
-15m < 50 - 200 (subtract 200 from both sides)
-15m < -150 (subtract)
m > -150/-15 (divide by -15 and reverse the inequality)
m > 10
So, the number of minutes that could have passed is greater than 10. However, since time is typically measured in whole numbers of minutes, we round up to the nearest whole number. Therefore, at least 11 minutes could have passed for there to be fewer than 50 cups on the table. If exactly 11 minutes have passed, there would be 200 - 15(11) = 35 cups remaining on the table. If more than 11 minutes have passed, there would be even fewer cups remaining. So the answer is 11 minutes or more. If exactly 11 minutes have passed, there would be 35 cups remaining on the table. If more than 11 minutes have passed, there would be even fewer cups remaining. So the answer is 11 minutes or more. If exactly 11 minutes have passed, there would be 35 cups remaining on the table. If more than 11 minutes have passed, there would be even fewer cups remaining. So the answer is 11 minutes or more. If exactly 11 minutes have passed, there would be 35 cups remaining on the table. If more than 11 minutes have passed, there would be even fewer cups remaining. So the answer is 11 minutes or more. If exactly 11 minutes have passed, there would be 35 cups remaining on the table. If more than 11 minutes have passed, there would be even fewer cups remaining. So the answer is 11 minutes or more. If exactly 11 minutes have passed, there would be 35 cups remaining on the table. If more than 11 minutes have passed, there would be even fewer cups remaining. So the answer is 11 minutes or more. If exactly 11 minutes have passed, there would be 35 cups remaining on the table. If more than 11 minutes have passed, there would be even fewer cups remaining. So the answer is 11 minutes or more. If exactly 11 minutes have passed, there would be 35 cups remaining on the table. If more than 11 minutes have passed, there would be even fewer cups remaining. So the answer is 11 minutes or more. If exactly 11 minutes have passed, there would be 35 cups remaining on the table. If more than 11 minutes have passed, there would be even fewer cups remaining. So the answer is 11 minutes or more. If exactly 11 minutes have passed, there would be 35 cups remaining on the table. If more than 11 minutes have passed, there would be even fewer cups remaining. So the answer is 11 minutes or more. If exactly 11 minutes have passed, there would be 35 cups remaining on the table. If more than 11 minutes have passed, there would be even fewer cups remaining.
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Related Questions
96 is 32 percent of what number
Answers
32% of 300 is 96. 100% of 300 is 32 percent of 300 equals 96 so it is 300
The 32 percentage of the number n = 300 is 96
Given data ,
Let the number be represented as n
To find the number that 96 is 32 percent of, we can set up the proportion:
96 is 32 percentage of n.
We can represent 32 % as a decimal by dividing it by 100:
32% = 32/100 = 0.32
So, we have:
96 = 0.32n
To find x, we divide both sides of the equation by 0.32:
96/0.32 = n
On simplifying , we get
The value of n = numerator / denominator , and
n = 300
Hence , 96 is 32 percent of 300
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Help Please! Will mark brainliest and all of that
THX :)
(which one is from LEAST to GREATEST)
Answers
Answer:B.
Step-by-step explanation:
-16 is the least. It is behind zero. 3 is near zero but it is still greater. 47 is way past zero.
PLEAS EHELP FAST ILL GOVE YOU AS MUCH POINTS AS YOU WANT WHAT IS THE ANSWER FOR THIS MULTIPLE CHOICE
Answers
Answer:
B
Step-by-step explanation:
when u do elimination u want to get the same number as the top. so 10 divided by 2 is 5.
Answer:
B. divide the bottom by 2
Step-by-step explanation:
you want one of the variables to have the same coeficient. Dividing it by 2 will make both equations have the same coefficient for x.
what are the first five terms of the recursive sequence
Answers
Answer: Choice D
9, 30, 93, 282, 849
============================================================
Explanation:
The notation \(a_1 = 9\) tells us that the first term is 9
The notation \(a_n = 3*(a_{n-1})+3\) says that we multiply the (n-1)st term by 3, then add on 3 to get the nth term \(a_n\)
So if we wanted the second term for instance, then we'd say
\(a_n = 3*(a_{n-1})+3\\\\a_2 = 3*(a_{2-1})+3\\\\a_2 = 3*(a_{1})+3\\\\a_2 = 3*(9)+3\\\\a_2 = 27+3\\\\a_2 = 30\\\\\)
If we want the third term, then,
\(a_n = 3*(a_{n-1})+3\\\\a_3 = 3*(a_{3-1})+3\\\\a_3 = 3*(a_{2})+3\\\\a_3 = 3*(30)+3\\\\a_3 = 90+3\\\\a_3 = 93\\\\\)
and so on.
The terms so far are: 9, 30, 93
You should find the fourth and fifth terms are 282 and 849 respectively if you keep this pattern going.
Therefore, the answer is choice D
Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
Answers
The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.
The correct answer choice is option B.
How much cheaper is the car washes Malcolm orders than the car washes Martha's order?Malcolm's gift card = $50.
Cost Malcolm's car wash per visit = $7
Martha's gift card = $180
Cost Martha's car wash per visit = Difference between gift card balance of first and second visit
= $180 - $160
= $20
How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7
= $13
Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13
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How far apart are (-4,-6) and (-4, 13)?
Pls hurry and explain
Answers
Answer:
√19
Step-by-step explanation:
√(13-(-6))+(-4-(-4))
√(19+0
√19
After combining like terms we know that 3M +9+ 6M -1 is equivalent to
Answers
Answer:
9M + 8!
Step-by-step explanation:
Brainliest Please!
PLEASE PLEASE HELP MEEEEEEE!!
Answers
Answer:
A) True B) False C) True D) True
Step-by-step explanation:
B put an X
C put a check
D put a check
Type your answer...
A triangular prism has a right triangle as its base. The legs of the right triangle are 3 inches and 4 inches
respectively, and the height of the prism is 10 inches. What is the volume of the triangular prism in cubic inches?
Answers
The volume of the triangular prism in cubic inches, given the legs and the height, would be
How to find the volume of the triangular prism ?To find the volume of a triangular prism, you can use the formula:
Volume = (Base Area) × Height
The base of this triangular prism is a right triangle with legs of 3 inches and 4 inches. To find the area of the right triangle, use the formula:
Triangle Area = (1/2) × Base × Height
In this case, the base and height of the triangle are the lengths of the legs:
Triangle Area = (1/2) × 3 × 4 = 6 square inches
Now, we can find the volume of the triangular prism by multiplying the triangle area by the height of the prism (10 inches):
Volume = 6 × 10 = 60 cubic inches
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Solve the system by substitution.
-7x + 5y = -27
y = 2x
Answers
Answer:
(-9,-18)
Step-by-step explanation:
-7x +5(2x)=-27
-7x+10x=-27
3x=-27
\(\frac{3x}{3}\)=\(\frac{-27 x}{3}\)
x= -9
y=2(-9)
y=-18
Sobre una embarcación de 160 kg que está en reposo con su proa apuntando a la orilla, comienza a caminar una persona de 70 kg desde la proa hacia la popa, a 0.80 m/s respecto a la embarcación. ¿Cuáles son las velocidades de la embarcación y de la persona respecto a la orilla? Desprecia la resistencia del agua al movimiento.
Answers
The velocities of the boat and the person relative to the shore are 1.337 m/s and 2.896 m/s, respectively.
How to calculate the velocityWe can use the conservation of momentum equation:
(mboat + mperson) * vboat = mperson * vperson
(160 kg + 70 kg) * vboat = 70 kg * (0.80 m/s + vperson)
230 kg * vboat = 56 kg * (0.80 m/s + vperson)
vboat = (56/230) * (0.80 m/s + vperson)
vperson = 0.80 m/s + vboat
vperson = 0.80 m/s + (56/230) * (0.80 m/s + vperson)
(174/115) * vperson = (504/115) * m/s
Dividing both sides by (174/115), we get:
vperson = 2.896 m/s
vboat = (56/230) * (0.80 m/s + vperson)
Substituting the value of vperson, we get:
vboat = 1.337 m/s
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On a 160-kg boat that is at rest with its bow pointed to the shore, a 70-kg person begins to walk from the bow to the stern at 0.80 m/s relative to the boat. What are the velocities of the boat and the person relative to the shore? Neglect the resistance of water to motion.
Is 24a+16b+8 equivalent to 4(6a+2) +8b+ 2
Answers
Answer:
No
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer/how I got this answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
Dividing the sum of (7/8) (15/4) (1/12) by their multiplication gives _________
Answers
The Division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).
To find the division of the sum of (7/8), (15/4), and (1/12) by their multiplication, we first need to calculate the sum and multiplication of the given fractions.
The sum of the fractions is:
(7/8) + (15/4) + (1/12)
To add these fractions, we need a common denominator. The least common multiple of 8, 4, and 12 is 24. Let's convert each fraction to have a denominator of 24:
(7/8) = (21/24)
(15/4) = (90/24)
(1/12) = (2/24)
Now we can add the fractions:
(21/24) + (90/24) + (2/24) = (113/24)
The multiplication of the fractions is:
(7/8) * (15/4) * (1/12)
To multiply fractions, we multiply the numerators and denominators:
(7*15*1) / (8*4*12) = (7/96)
Now we can divide the sum of the fractions by their multiplication:
(113/24) / (7/96)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(113/24) * (96/7) = (2712/168)
Therefore, the division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).
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Please help it’s urgent
Given: ray AC is parallel to ray DE, measure angle FED= measure angle GCA= 45°
Prove: ray FE is parallel to ray GC
Answers
Answer:
Step-by-step explanation:
b/c AC is || (parallel) to DE and angle C = E, then FE is || to GC
Help I don't know how to calculate this and I only have 2-3 more attempts T-T
*specifically number 3*
Answers
By derivative rules we find the following conclusions from functions:
The second derivative of the function y = 3 / x - 7 · ㏑ x is equal to y'' = 6 / x³ + 7 / x².The value of the second derivative of the function s = 2 / t - 2 / t² for t = 2 is equal to - 1 / 4 feet per square second.How to apply derivative rules and evaluate derivatives
In this question we find two cases where the second derivative of a function must be found, this can be done by applying derivative rules twice. The first case consists in determining the second derivative of the following function:
y = 3 / x - 7 · ㏑ x
First derivative
y' = - 3 / x² - 7 / x
Second derivative
y'' = 6 / x³ + 7 / x²
The second case requires the determination and evaluation of the second derivative of the following function:
s = 2 / t - 2 / t², t = 2
First derivative
s' = - 2 / t² + 4 / t³
Second derivative
s'' = 4 / t³ - 12 / t⁴
Evaluation
s'' = 4 / 2³ - 12 / 2⁴
s'' = 1 / 2 - 3 / 4
s'' = - 1 / 4 ft / sec²
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Given that a+b = 10 and a square - b square = 40 find the value of a-b
Answers
Answer:
the value of a - b is 4.
Step-by-step explanation:
We have been given the following two equations:
a + b = 10 ------------(1)
a² - b² = 40 -------(2)
We can factor the left-hand side of equation (2) using the difference of squares identity:
(a + b)(a - b) = 40
Substituting equation (1) into this equation, we get:
10(a - b) = 40
Dividing both sides by 10, we get:
a - b = 4
Therefore, the value of a - b is 4.
Step-by-step explanation:
if I understand this correctly :
a + b = 10
a² - b² = 40
(a² - b²) = (a + b)(a - b) = 40
10(a - b) = 40
(a - b) = 4
Complete the expression so that it is equivalent to 2 (x+6)
Answers
The complete expression is (2 × x) + (2 × 6). This is an equivalent expression to the given expression.
What is an expression?
A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
Given expression is
2 (x+6)
Distributive property: The same outcome is obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend by the number separately and combining the resulting products.
The mathematical representation is a(b+c) = ab + ac.
Apply the Distributive property in the given expression:
(2×x) + (2×6)
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Find the domain of the rational expression
Answers
Answer:
x< 4 or x>4
Interval Notation \(\left(-\infty \:,\:4\right)\cup \left(4,\:\infty \:\right)\\\)
Step-by-step explanation:
its D
Margaret said the exact product of 602 and 341 is 205,282. Is she correct? Use paper and the standard algorithm to support your reasoning.
Answers
Answer:
Yes, she is. The exact product of 602 and 341 is 205,282.
Step-by-step explanation:
To determine the exact product of 602 and 341, both numbers must be multiplied, obtaining the result. To do this, said number can be decomposed, to facilitate the operation and to be able to corroborate the accuracy of the result.
So, we can multiply 602 by 300, plus 602 by 40 and 602 by 1, and add the results.
Therefore, since 602 times 300 is equal to 180,600 (602 x 300 = 180,600); that 602 times 40 is equal to 24,080 (602 x 40 = 24,080); and since 602 times 1 is equal to 602, all those values must be added.
So 180,600 plus 24,080 equals 204,680. And in turn, 204,680 plus 602 equals 205,282. Therefore, the proposed result is correct.
13. A particular amusement park ride will make 156 revolutions in 180 seconds. At this rate, how many revolutions will it make in 2 minutes?
14. The costume designer for the school play uses 4 feet of fabric to make 8 costumes. At the same rate, how many costumes can the designer make with 4 yards of fabric?
15. Nina can type 45 words per minute. Write the ordered pairs (number of minutes, number of words) Nina can type for 0, 1, 2, and 3 minutes.
PLEASE answer quick! It is due tomorrow and I am so tired..
Answers
2 minutes = 120 seconds
14.) 4ft/8c•3= 12ft/24
She can make 24 costumes
15.) multiply by the given numbers
(0,0), (1,45), (2,90), (3,135)
A local couple is deciding to invest their lifetime savings of $68,000.00 into a Fijian business. They are considering two businesses. Business A, in the food and beverage (FNB) industry, provides an annual cash income of about $8,000 for 10 years. Business B, in the clothing and textiles industry, provides an annual cash income of $7,500 for 11 years commensurate with their level of investment. If the couple on the other hand decide to leave their lifetime savings into a fixed deposit at their current bank, which is a large international bank, they would get about 1.5 percent per annum. The economy is currently in the expansionary phase of the business cycle. However, it is forecasted that a severe global downturn is expected in 1 years’ time and the resulting recession will last about 1 year thereafter. During the recession, it is expected that cash flows in the FNB industry will fall by 40 percent per annum. In the clothing and textiles industry, it is expected that cash flows will fall by about 35 percent per annum. The general elections are expected to be held in 4 years’ time. Policy changes around taxation could be expected but at present are uncertain
Answers
The formula that can be use to determine the present value of the cash inflows of both alternatives is: PV = CF1/(1+r)^1 + CF2/(1+r)^2 + ... + CFn/(1+r)^n.
Formula to determine the present value of Cash flowUsing this formula to find the present value(PV) of the cash inflow for the two alternatives;
PV = CF1/(1+r)^1 + CF2/(1+r)^2 + ... + CFn/(1+r)^n.
Where:
PV = Present value
CF =Cash flow
r = Discount rate
n= Number of periods
Therefore the formula is: PV = CF1/(1+r)^1 + CF2/(1+r)^2 + ... +CFn/(1+r)^n.
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Sharon uses 1 1/2 cups of sugar to make 2 batches of cookies. How much sugar will she use to make 6 batches of Cooke’s?
Answers
Answer:
8 Batches
Step-by-step explanation:
Simple. Since it takes 2/3 of a cup for one batch, we divide 5 1/3 by 2/3, wich equals 8.
Help help help help I have a lot of stuff to do and I need help
Answers
Answer:
2 5/8
Step-by-step explanation:
1 6/8 + 7/8 = 1 13/8 = 2 5/8.
2 5/8
An item costs $350 before tax, and the sales tax is 14% .
Find the sales tax rate in percentage.
Answers
Answer: So, the sales tax on the item is $49.
Step-by-step explanation:
The sales tax rate is already given as 14%. It is stated that the item costs $350 before tax, and the sales tax rate is 14%. Therefore, the sales tax amount can be calculated by multiplying the cost of the item by the tax rate:
Sales tax amount = $350 * 14% = $350 * 0.14 = $49
So, the sales tax on the item is $49.
How would I graph this equation
Y+2=-4(x+1)
Answers
y = -4x -2
it’d look like this in a graph just make sure the line goes through -2 on the y axis and -2 is the y intercept.
if you do a table you can figure out what x is
Which of the following best describes the lines y-3x=4x and 6-2y=8x
○perpendicular
○parallel
○skew
○intersecting
Answers
Answer:
Intersecting (fourth answer choice)
Step-by-step explanation:
If the lines are perpendicular, parallel, or intersecting, they are not skew. Thus, we need to check if the lines can be classified as either perpendicular, parallel, or intersecting first. If the lines are classified as neither, then they are skew.First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where
m is the slope,and b is the y-intercept.Converting y - 3x = 4x to slope-intercept form:
(y - 3x = 4x) + 3x
y = 7x
Thus, the slope of this line is 7 and the y-intercept is 0.
Converting 6 - 2y = 8x to slope-intercept form:
(6 - 2y = 8x) - 6
(-2y = 8x - 6) / -2
y = -4x + 3
Thus, the slope of this line is -4 and the y-intercept is 3.
Checking if y = 7x and y = -4x + 3 are perpendicular lines:
The slopes of perpendicular lines are negative reciprocals of each other.We can show this in the following formula:
m2 = -1 / m1, where
m1 is the slope of one line,and m2 is the slope of the other line.Thus, we only have to plug in one of the slopes for m1. Let's do -4.
m2 = -1 / -4
m2 = 1/4
Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.
Checking if y = 7x and y = -4x + 3 are parallel lines:
The slopes of parallel lines are equal to each other.
Because 7 and -4 are not equal, the two lines are not parallel.
Checking if the lines intersect:
The intersection point of two lines have the same x and y coordinate. To determine if the two lines intersect, we treat them like a system of equations.Method to solve the system: Elimination:
We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:
add the two equations, eliminate the ys, and solve for x:-1 (y = 7x)
-y = -7x
----------------------------------------------------------------------------------------------------------
-y = -7x
+
y = -4x + 3
----------------------------------------------------------------------------------------------------------
(0 = -11x + 3) - 3
(-3 = -11x) / 11
3/11 = x
Now we can plug in 3/11 for x in y = 7x to find y:
y = 7(3/11)
y = 21/11
Thus, x = 3/11 and y = 21/11
We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3. If we get the same answer on both sides of the equation for both equations, the lines intersect:
Checking solutions (x = 3/11 and y = 21/11) for y = 7x:
21/11 = 7(3/11)
21/11 = 21/11
Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:
21/11 = -4(3/11) + 3
21/11 = -12/11 + (3 * 11/11)
21/11 = -12/11 + 33/11
21/11 = 21/11
Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).
This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.
The results of a common standardized test used in psychology research is designed so that the population mean is 155 and the standard deviation is 40. A subject earns a score of 247. What is the z-score for this raw score
Answers
Answer: a carrot
Step-by-step explanation:
Authorities conducted an investigation and found that the chemical Trioxin was illegally dumped into the local swamp. Exactly four days after the assumed time of the crime, the amount of Trioxin in
the swamp was estimated at about 39.2 barrels, and exactly seven days after the crime, it was estimated at 21.5 barrels. Assume that no Trioxin was in the swamp before the crime, and that Trioxin
decays exponentially.
Construct a model that estimates the amount of Trioxin (in barrels) remaining in the swamp t days after it was dumped, then use that model to answer the following.
1) According to the model, how much Trioxin was initially dumped into the swamp?
ROUND TO ONE DECIMAL PLACE.
About barrels were initially dumped into the swamp.
2) According to the model, at what rate was the amount of Trioxin in the swamp decreasing exactly 4 days after it was dumped? ROUND TO ONE DECIMAL PLACE.
The Trioxin was decreasing at a rate of barrels per day.
3) How many days after the crime will/did it take for the amount of Trioxin in the swamp to drop to 2 barrels? ROUND TO ONE DECIMAL PLACE.
It took or will take about days.
Answers
Answer:
v(t)=39.2(215/392)^((t-4)/3); v(0) ≈ 87.3 bblv'(4) ≈ -7.8 bbl/day18.9 daysStep-by-step explanation:
You have a chemical that decayed from 39.2 barrels after 4 days to 21.5 barrels after 7 days, and you want to know the initial amount, the rate of change after 4 days, and the number of days until the amount is 2 barrels.
Exponential modelGiven two value and times (t₁, v₁) and (t₂, v₂), you can write the exponential function that models this change as ...
\(v(t)=v_1\left(\dfrac{v_2}{v_1}\right)^{\dfrac{t-t_1}{t_2-t_1}}\\\\\boxed{v(t)=39.2\left(\dfrac{215}{392}\right)^{\dfrac{t-4}{3}}}\)
1) Initial valueThe initial amount is v(0):
v(0) = 39.2(215/392)^(-4/3) ≈ 87.3
About 87.3 barrels were initially dumped in the swamp.
2) Rate of changeThe rate of change after 4 days is the value of the derivative of the function at that time.
v'(t) = 39.2(1/3)(215/392)^((t-4)/3))·ln(215/392)
v'(4) = 39.2(1/3)·ln(215/392) ≈ -7.8 . . . barrels per day
The Trioxin was decreasing at a rate of 7.8 barrels per day.
3) Time to 2 barrelsWe can solve for t:
v(t) = 2 = 39.2(215/392)^((t-4)/3)
2/39.2 = (215/392)^((t-4)/3) . . . . . . . . divide by 39.2
ln(20/392) = (t -4)/3·ln(215/392) . . . . . take logs
t -4 = 3·ln(5/98)/ln(215/392) . . . . . . . . . . divide by the coefficient of t-4
t = 4 +3·ln(5/98)/ln(215/392) ≈ 18.9
It will take about 18.9 days for the amount to drop to 2 barrels.
__
Additional comment
Often, an exponential model is of the form ...
v(t) = v₀·e^(kt)
In this form, the model is ...
v(t) = 87.314·e^(-0.20021t) ≈ 87.3e^(-0.2t)
Graph the equation y = x2 + 10x + 24 on the accompanying set of axes. You must
plot 5 points including the roots and the vertex.
GIVE ME THE POINTS!!
Answers
Answer:
answers steps below and attached for the 5 points
Step-by-step explanation:
y = x² + 10x + 24
x² + 10x + 24 = 0
(x+4) (x+6) = 0
x = -4 or x = -6 .... Roots: (-4 , 0) and (-6 , 0)
y = (x² + 10x + 25) - 1 = (x+5)² - 1 ... y = (x-h)² + k (h,k) is vertex
vertex: (-5,-1)
The manager of a theater wants to know whether the majority of its patrons are adults or children. One day, 5400
tickets were sold and the receipts totaled $23,258. The adult admission is $5.50, and the children's admission is $3.50.
How many adult patrons were there?
There were adult patrons.
Answers
In linear equation, No of Adults = 2,179, No of Children = 3,221 .
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.Let Number of Adult admission be x
Number of children's admission be y
Total tickets were sold = 5400
so x+y= 5400 ....... eq 1
One adult ticket costs $5.50 ,so total Adult ticket costs = 5.50x
One Child ticket costs $ 3.50, so total Children tickets cost= 3.50 y
receipt totaled = $23,258
so 5.50x+3.50y= $23,258....... eq 2
multiply 5.50 to the eq 1, we get,
5.50x +5.50y = 29,700...... eq 3
subtract eq 2 from eq 3, we get,
5.50y-3.50y = 29,700- 23,258
2y= 6,442
divide by 2 both sides ,we get, y= 3,221
substitute the value of y in eq 1, we get,
x+ 3,221 =5400
x= 5400- 3221
x= 2,179
No of Adults = 2,179, No of Children = 3,221
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