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.

There were 172 guests that were children and 278 guests that were adults

Step-by-step explanation:

Step 1: State what is known

It is $25 per adult

It is $12 per child

The made $9014 dollars

There were 450 guests

Step 2: Define equations

25y + 12x = 9014 1

x + y = 450 2

Step 3: Rearrange equation 2 for x

x + y = 450

x = 450 - y 3

Step 4: Substitute 3 into 1 for y and solve for y

25y + 12(450 - y) = 9014

25y + 5400 - 12y = 9014

13y = 3614

y = 3614/13

y = 278

Step 5: Substitute y = 278 into 3 to solve for x

x = 450 - (278)

x = 172

Therefore 172 children and 278 adults visited the museum

step-by-step explanation:

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