Question

The admission fee at a fair is $3.25 for children and $6.75 for adults. On a certain day, 870 people enter the fair and $3,772.50 is collected. Write a system of linear equations that you can use to determine how many children and adults attended. Be sure to define your variables. Solve the system. SHOW YOUR WORK PLEASE!

Answer 1

Total number of children = 600

Total number of adults = 270

Step-by-step explanation:

Admission fee at fair for children = $3.25

Admission fee at fair for adults = $6.75

Total people entered the fair = 870

Collected amount = $3,772.50

Let X be the number of children and Y be the number of adults.

We have total of 870 people

X + Y = 870 -------------- Equation 1

Collected amount = $3,772.50

3.25 X + 6.75 Y = 3,772.50------------Equation 2

Multiplying equation 1 with 3.25,

3.25 X + 3.25 Y = 2827.5---------------Equation 3

Equation 2 - Equation 3,

(3.25 X + 6.75 Y) - ( 3.25 X + 3.25 Y) = 3,772.50 - 2827.5

3.5 Y = 945

Y = 270 adults.

Substituting in equation 1

X + 270 = 870

X = 600 children.

So Total number of children = 600

Total number of adults = 270