A local museum charges $25 per adult and $12 per child for admission fees. At the end of a day, the museum made $9,014 in total

Question

2 months ago

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A local museum charges $25 per adult and $12 per child for admission fees. At the end of a day, the museum made $9,014 in total

admission revenue, not including sales tax, and had a total of 450 guests. The system of equations below can be used to model the number of guests that were children, x, and the number of guests that were adults, y.

Mathematics

1 answer:

tester [12.3K] · Answer 1 · 2026-03-20T15:29:28+03:00

Answer:

There were 172 guests who were children and 278 adults in attendance

Step-by-step explanation:

Step 1: State whatat is known

An admission fee of $25 is charged for each adult

There is a $12 fee for each child

The total revenue was $9014

There was a total of 450 attendees

Step 2: Define equations25y + 12x = 9014 -----1

x + y = 450 ------------2

Step 3: Rearrangeequation2 for xx + y = 450x = 450 - y --------------3Step4

:

Substitute

3

into

1

for y and solve for y25y + 12(450 - y) = 901425y + 5400 - 12y = 901413y = 3614y = 3614/13y = 278Step5:Substitute y = 278into 3

to

solve

for

x

x = 450 - (278)

x = 172

This concludes that there were 172 children and 278 adults who attended the museum