Question

Columbia Theater Company reviewed 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

If 48 adults and 26 children attended the matinee on Sunday, the theater raised $ 514 from ticket sales.

Explanation:

A system of linear equations is a set of linear equations that have more than one unknown, which are related through the equations.

In this case, being:

• A: adult ticket price
• C: child ticket price.

The system of equations is:

`\left \{ {{83*A+42*C=874} \atop {102*A+67*C=1151}} \right.`

The substitution method consists of isolating one of the two unknowns in one equation to replace it in the other equation. In this case you isolate C from the first equation:

83*A + 42*C= 874

42*C= 874 - 83*A

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

Substituting this expression in the second equation:

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

and solving:

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

Multiply through by 42

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

4,284*A + 67*(874-83*A)= 48,342

4,284*A + 58,558 - 5,561*A= 48,342

4,284*A - 5,561*A= 48,342 - 58,558

-1,277*A= -10,216

`A=(-10,216)/(-1,277)`

A= 8

Knowing that:
`C=(874 - 83*A)/(42)` then:

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

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

`C=(210)/(42)`

C= 5

The price of an adult ticket is $8 and a child is $5. If 48 adults and 26 children attended the matinee on Sunday, then:

$8*48 adults + $5* 26 childen= $514

If 48 adults and 26 children attended the matinee on Sunday, the theater raised $ 514 from ticket sales.