You are the CEO and Manager of MathFair (a Math based theme park, obviously) that charges: children $2, adults $5, and vets $3. You are looking over the books for last weekend. 1,900 people came to the park. You took in $6,300. There were 100 unaccompanied children (that is, the number of children was 100 more than the number of adults and vets combined). How many children, adults, and vets visited Math Fair last weekend

700 adults

800 children

400 vets

Explanation:

children $2

adults $5

vets $3

1,900 came to the park, total revenue = $6,300

number of children was 100 more than adults

Let:

C = number of children

A = number of adults

V = number of vets

2C + 5A + 3V = 6,300

C + A + V = 1,900

C = A + 100 (we can replace C with A)

2 (A + 100) + 5A + 3V = 6,300 ⇒ 2A + 200 + 5A + 3V = 6,300

7A + 3V = 6,100

A + 100 + A + V = 1,900 ⇒ 2A + V + 100 = 1,900

2A + V = 1,800

7A + 3V = 6,100

2A + V = 1,800 ⇒ V = 1,800 - 2A (we can replace V)

7A + 3 (1,800 - 2A) = 6,100

7A + 5,400 - 6A = 6,100

A = 6,100 - 5,400 = 700

C = A + 100 = 800

V = 1,900 - 700 - 800 = 400