SOLUTION: If 129 people attend a concert and tickets for adults cost $2.25 while tickets for children cost $1.5 and total receipts for the concert was $233.25, how many of each went to the c

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Question 1204597: If 129 people attend a concert and tickets for adults cost $2.25 while tickets for children cost $1.5 and total receipts for the concert was $233.25, how many of each went to the concert?
Found 3 solutions by ikleyn, josgarithmetic, math_tutor2020:
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
If 129 people attend a concert and tickets for adults cost $2.25
while tickets for children cost $1.5 and total receipts for the concert was $233.25,
how many of each went to the concert?
~~~~~~~~~~~~~~~~~~~~~ 

x adults; (129-x) children


Write the total money equation

    2.25x + 1.50*(129-x) = 233.25   dollars.


Simplify and find x

    2.25x + 1.50*129 - 1.50x = 233.25

    2.25x - 1.50x = 233.25 - 1.50*129

        0.75x     =     39.75

            x     =     39.75/0.75 = 53.


ANSWER.  53 adults and 129-53 = 76 children.


CHECK.  53*2.25 + 76*1.50 = 233.25  dollar, total money.   ! correct !

Solved.

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Is everything clear to you in my solution ?



Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
                 PRICE         HOW MANY        RECEIPT SALES
Adults            2.25            y                2.25y
Children          1.5           129-y              1.5(129-y)
TOTAL                            129                233.25

--------simplify and solve for y.

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Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Let's say there are 129 adults in attendance.

That would bring in 2.25*129 = 290.25 dollars in revenue.
This value is to large compared to the actual revenue of $233.25

We need to decrease the revenue by 290.25 - 233.25 = 57 dollars.

We'll need to replace some adults with children to bring the revenue down.
Each time we replace 1 adult with 1 child, the revenue drops by $0.75, aka 75 cents, because 2.25 - 1.50 = 0.75

n = number of times we replace 1 adult with 1 child
0.75n = total decrease in revenue
0.75n = 57
n = 57/0.75
n = 76
We'll have 76 instances where we replace 1 adult with 1 child.

The 129 adults drops to 129-76 = 53 adults.
The 0 children increases to 0+76 = 76 children

Check:
53 adults + 76 children = 129 people total
53 adults bring 53*2.25 = $119.25 in revenue
76 children bring 76*1.5 = $114 in revenue
total revenue = 119.25+114 = 233.25
Or as a shortcut we could say: 53*2.25 + 76*1.5 = 233.25
The answers are confirmed.



Summary
53 adults
76 children
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