Question

Columbia theater company reviews their receipts from opening weekend. They sold 83 adult tickets and 42 child tickets on Friday night, collecting a total of $874. On Saturday night, they collected $1151 from 102 adults and 67 children. If 48 adults and 26 children attended the matinee on Sunday, how much money did the theater collect from ticket sales?

Answer 1

They made a sales for $514

Explanation:

Represent Adult with A

Represent Children with C

Given

Friday Night: 83A + 42C = 874

Saturday Night: 102A + 67C = 1151

Required

Determine 48A + 26C

`83A + 42C = 874`

`102A + 67C = 1151`

Make C the subject in the first equation

`83A + 42C = 874`

`42C= 874 - 83A`

`C = (874 - 83A)/(42)`

Substitute this for C in the second equation

`102A + 67C = 1151`

`102A + 67 * (874 - 83A)/(42) = 1151`

Multiply through by 42

`42 * 102A + 42 * 67 * (874 - 83A)/(42) = 1151 * 42`

`42 * 102A + 67 (874 - 83A) = 1151 * 42`

`4284A + 58558 - 5561A = 48342`

Collect Like Terms

`4284A - 5561A = 48342 - 58558`

`-1277A = -10216`

Solve for A

`A = (-10216)/(-1277)`

`A = 8`

Recall that

`C = (874 - 83)/(42)`

`C = (874 -83 * 8)/(42)`

`C = (874 -664)/(42)`

`C = (210)/(42)`

`C = 5`

Solving for 48A + 26C

`48A + 26C = 48 * 8 + 26 * 5`

`48A + 26C = 384 + 130`

`48A + 26C = 514`

Hence, they made a sales for $514