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?

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

Step-by-step 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:

The system of equations is:

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

Substituting this expression in the second equation:

and solving:

Multiply through by 42

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= 8

Knowing that: then:

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.

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