Question

Admission to a museum is $10 for each adult and $5 for each child. If a group oh 30 people pays a total of $175 in admission how many adults are in the group?

Answer 1

let x = number of adults
let y = number of children

There are 30 people in the group, so x+y = 30

The total cost is $175, so 10x + 5y = 175

10x + 5y = 175
Divide by 5:
2x + y = 35

Now subtract the two equations:
2x + y = 35
x + y = 30
x = 5

Substitute x into one of the equations to find y.

5 + y = 30
y = 25

Now plug both values into the other equation to check your work.

2(5) + 25 = 35
10 + 25 = 35
35 = 35

Your answers are correct.