The admission fee at an amusement park is $4.50 for children and $13.00 for adults. On
a certain day, 328 people entered the park, and the admission fees collected totaled
$3,176.00. How many children and how many adults were admitted?

The admission fee at an amusement park is $4.50 for children and $13.00 for adults
On a certain day, 328 people entered the park, and the admission fees collected totaled $3,176.00

Find how many children and how many adults were admitted

Assume that the number of children is x and the number of adults is y

∵ There were x children in that day

∵ There were y adults in that day

∵ 328 people entered the park in that day

∴ x + y = 328 ⇒ (1)

∵ The admission fee for a children is $4.50

∵ The admission fee for an adult is $13.00

∵ The total admission fees collected is $3,176.00

∴ 4.5 x + 13 y = 3,176 ⇒ (2)

Let us solve the system of equations to find x and y

Multiply equation (1) by -13 to eliminate y

∴ -13 x - 13 y = -4,264 ⇒ (3)

- Add equation (2) and (3)

∴ -8.5 x = -1,088

- Divide both sides by -8.5

∴ x = 128

Substitute the value of x in equation (1) to find the value of y

∵ 128 + y = 328

- Subtract 128 from both sides

∴ y = 200

There were 128 children and 200 adults admitted

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