SOLUTION: If 110 people attend a concert and tickets for adults cost $3.5 while tickets for children cost $3.25 and total receipts for the concert was $370, how many of each went to the conc

Question 1200422: If 110 people attend a concert and tickets for adults cost $3.5 while tickets for children cost $3.25 and total receipts for the concert was $370, how many of each went to the concert?
Found 2 solutions by math_tutor2020, josgarithmetic:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answer: 50 adults, 60 children

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Explanation:

I'll go over 3 methods to solving this problem.

Method 1

Let's say that all 110 people were adults
110 adults --> 110*3.50 = 385 dollars total

But the total cost should be $370.
The gap from 385 to 370 is 385-370 = 15.

Each time we remove an adult, and add a child, then the net change in revenue is -0.25 (since 3.25-3.50 = -0.25)
In other words, the revenue goes down by $0.25 aka 25 cents, each time we replace an adult with a child.

x = number of adults that are replaced with children
0.25x = net decrease in cost
0.25x = 15
x = 15/0.25
x = 60
We must remove 60 adults and replace them with 60 children.

We go from 110 adults to 110-60 = 50 adults.
We go from 0 children to 0+60 = 60 children.

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Method 2

a = number of adults
110-a = number of children

3.50a = revenue from the adults
3.25(110-a) = revenue from the children
3.50a+3.25(110-a) = total revenue

3.50a+3.25(110-a) = 370
3.50a+357.5-3.25a = 370
0.25a+357.5 = 370
0.25a = 370-357.5
0.25a = 12.5
a = 12.5/0.25
a = 50
110-a = 110-50 = 60

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Method 3

x = number of adults
y = number of children

x+y = 110 total people
3.50x+3.25y = 375 total revenue

Use a graphing app like Desmos to plot each of those equations.
The two lines intersect at (x,y) = (50,60) to indicate x = 50 adults and y = 60 children.

Here's the link to the interactive graph
https://www.desmos.com/calculator/zmecbj4vep

Feel free to explore other methods to solving this type of problem.

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Check:
1 adult = $3.50
50 adults = 50*$3.50 = $175
1 child = $3.25
60 children = 60*$3.25 = $195
50 adults + 60 children = 110 people total
50 adults + 60 children = $175 + $195 = $370
The answers are fully verified.

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
This kind been done thousands of times.
50 adults
60 children

If choose x for how many children, then ; solve this and interpret...
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