SOLUTION: The admission fees at an amusement park are $4.25 for children and $6.00 for adults. On a certain day, 282 people entered the park, and the admission fees collected totaled $1,391.
Question 1202435: The admission fees at an amusement park are $4.25 for children and $6.00 for adults. On a certain day, 282 people entered the park, and the admission fees collected totaled $1,391.00. How many children and how many adults attended the amusement park that day?
There were children and adults that attended the amusement park that day. Found 2 solutions by math_tutor2020, josgarithmetic:Answer by math_tutor2020(3816) (Show Source):
You can put this solution on YOUR website!
If all 282 people were adults, then the total admission fees collected would be 6*282 = 1692 dollars.
This amount is too large compared to $1391. The gap is 1692-1391 = 301 dollars.
Let's replace some adults with children.
For each adult replaced with a child, the net amount collected goes down by 6-4.25 = 1.75 dollars per person.
Doing this x number of times means the total amount goes down by 1.75x dollars.
We want this decrease to go down by the gap 301 found earlier.
1.75x = 301
x = 301/1.75
x = 172
We must remove 172 adults and replace them with 172 children.
282 adults drops down to 282 - 172 = 110 adults
0 children increases to 0+172 = 172 children
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An alternative is to solve this system of equations
c+a = 282
4.25c+6a = 1391
where,
c = number of children
a = number of adults
c+a = 282 solves to c = 282-a
That is then substituted into the other equation to get 4.25(282-a)+6a = 1391
I'll skip the steps but you should get a = 110 and it leads to c = 172.
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Check:
172 children + 110 adults = 282 people total
P = revenue from the children
P = 172*4.25 = 731 dollars
Q = revenue from the adults
Q = 110*6 = 660 dollars
P+Q = total revenue
P+Q = 731+660
P+Q = 1391 dollars total revenue
We have confirmed the solutions.
You can put this solution on YOUR website! ---------------------------------
...,$4.25 for children and $6.00 for adults. On a certain day, 282 people entered the park, and the admission
fees collected totaled $1,391.00.
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