Question

A local theater is selling tickets for their upcoming production. They offer 3 different ticket

Answer 1

The given costs for the different combinations of tickets of $132, $201, and $88, finding the solution for the system gives;

The cost of a children's ticket = $63

The cost of an ticket = $(-19)

The cost of a senior ticket = $44

How can the system of equations be found?

Let x represent the cost of children tickets, y represent the cost of adult tickets and let z represent the cost of senior tickets.

The following system of equations can be obtained

• 2•x + 2•y + z = 132...(1)
• 3•x + 4•y + 2•z = 201...(2)
• 2•x + 2•y = 88...(3)

Therefore;

2•x + 2•y + z = 132

88 + z = 132

• z = 132 - 88 = 44

Therefore;

The cost of a senior ticket, z = $44

Multiplying equation (3) by 2 and subtracting equation (2) from the result gives;

2×(2•x+2•y) - (3•x+4•y+2•z) = x-2•z

2 × 88 - 201 = -25

Therefore;

x - 2•z = -25

x = 2•z - 25

Which gives;

• x = 2 × 44 - 25 = 63

The cost of a children ticket, x = $63

From equation (3), we have;

2•x + 2•y = 88

2•y = 88 - 2×63

• y = (88 - 2×63) ÷ 2 = -19

The cost of an adult ticket, y = $(-19)

Learn more about solving simultaneous equations here:

brainly.com/question/15165519

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