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Question 1203890: If 68 people attend a concert and tickets for adults cost $3.75 while tickets for children cost $2 and total receipts for the concert was $195.5, how many of each went to the concert?
Found 3 solutions by mananth, MathLover1, math_tutor2020:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! If 68 people attend a concert and tickets for adults cost $3.75 while tickets for children cost $2 and total receipts for the concert was $195.5, how many of each went to the concert?
68 people attend a concert
let x adults attend the concert . tickets for adults cost $3.75
Let y children attend the concert . Tickets for children cost $2
Number attended equation
x+y=68...........................................(1)
Receipts equation
3.75x + 2y = 195.5.............................(2)
Multiply (1) by 2 and subtract (2)
2x+2y = 136
3.75x +2y= 195.5 ( From (2))
-1.75x = -59.5
x = -59.5/-1.75
x=34
y =68-34 = 34
34 adults and 34 children attended the concert.
Answer by MathLover1(20849)  (Show Source):
Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
Answers: 34 adults, 34 children
Explanation
Consider the hypothetical scenario that all 68 people are adults.
If so, then 68*3.75 = 255 dollars would be the revenue.
However, the actual money pulled in was $195.50
The gap is 255-195.50 = 59.50
We must reduce the revenue by $59.50 to arrive at the correct revenue.
Each time we replace an adult with a child, the net revenue will go down by $1.75 because 3.75 - 2 = 1.75
n = number of times an adult is replaced by a child
1.75n = decrease in revenue
1.75n = 59.50
n = 59.50/1.75
n = 34
If all 68 people were adults, then we must replace 34 of them with children, so that the revenue drops by $59.50 to arrive at $195.50
68 adults ---> 68-34 = 34 adults
0 children ---> 0+34 = 34 children
There are an equal number of adults and children.
Check:
34 adults + 34 children = 68 people total
34 adults --> 34*($3.75) = $127.50
34 children --> 34*($2) = $68
total money = 127.50+68 = 195.50 dollars
The answers have been confirmed.
Another approach would be to graph the equations
x+y = 68
3.75x+2y = 195.50
to find the point of intersection is (x,y) = (34,34)
Desmos and GeoGebra are two graphing options I recommend.
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