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15 February, 12:40

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

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  1. 15 February, 14:37
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    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
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