Write a system of equations to describe the situation below, solve using elimination, and fill in
the blanks.
The manager at a community pool is looking over receipts. On a certain Monday, the pool had
16 children and 42 adults, which brought in $142. That same week on Tuesday, 24 children
and 26 adults came to the pool, which brought in $102. What are the admission prices for
children and adults?

Question

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Respuesta :

rspill6 rspill6 · Answer 1 · 2021-12-13T20:28:01+01:00

Answer: Child is $1 and Adult is $3, per person.

Step-by-step explanation:

We have two unknowns, so we need at least two equations. Let C and A stand for the price of a ticket for a child and an adult, respectively.

The income for Monday and Tuesday can be calculated:

Monday: 16C + 42A = $142

Tuesday: 24C + 26A = $102

Rearrange the second equation to isolate one of the variables. I'll pick C:

24C + 26A = $102

C = ($102 - 26A)/24

Now use this expression for C in the first equation

16C + 42A = $142

16(($102 - 26A)/24) + 42A = $142

(1632 - 416A)/24 + 42A = $142

(68 - 17.3333A + 42A = $142

24.6667A = 74

A = 3 [The price of an adult pool admission is $3]

Use this value in either equation to find the price of a child's admission:

24C + 26A = $102

24C + 26*($3) = $102

24C = 102 - 78

C = $1 [The price of a child's admission to the pool is $1]

Check to see if these prices satisfy both equations:

Monday: 16C + 42A = $142

Tuesday: 24C + 26A = $102

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Monday: 16*(1) + 42*(3) = $142 ? YES

Tuesday: 24*(1) + 26*(3) = $102 ? YES

Child is $1 and Adult is $3, per person.