Algebra

The admission fee at a local zoo is
$1.50 for children and
$4.00 for adults. On a certain day,
2200 people enter the zoo and
$4,550.00 is collected. How many children and how many adults attended?

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  1. c+a = 2200
    1.50c + 4.00a = 4550.00

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  2. c = children

    a = adults

    2200 people enter the zoo mean :

    c + a = 2200

    $4,550.00 is collected mean :

    1.5 c + 4 a = 4550

    Now you must solve system:

    c + a = 2200

    1.5 c + 4 a = 4550

    c + a = 2200 Subtract c to both sides

    c + a - c = 2200 - c

    a = 2200 - c

    1.5 c + 4 a = 4550

    1.5 c + 4 ( 2200 - c ) = 4550

    1.5 * c + 4 * 2200 - 4 c = 4550

    1.5 * c + 8800 - 4 c = 4550

    - 2.5 c + 8800 = 4550 Subtract 8800 to both sides

    - 2.5 c + 8800 - 8800 = 4550 - 8800

    - 2.5 c = - 4250 Divide both sides by - 2.5

    c = - 4250 / - 2.5

    c = 1700

    a = 2200 - c = 2200 - 1700 = 500

    1700 children and 500 adults

    Proof :

    c + a = 1700 = 2200

    $ 1.5 * c + $ 4 * a =

    $ 1.5 * 1700 + $ 4 * 500 =

    $ 2550 + $ 2000 = $ 4550

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  3. Thank you.

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