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13 December, 17:32

Andrew has a collection of soda bottles. Some of them are 12 ounce bottles, and others are 16 ounce bottles. If the collection contains 20 bottles, which hold a combined 300 ounces, how many of the soda bottles are 12-ounce bottles?

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  1. 13 December, 19:35
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    Use a for the 12 ounce bottles and b for the 16 ounce bottles. Now make two equations, one to show total ounces and one total bottles.

    12a + 16b = 300 (12 ounces in a number of bottles plus 16 ounces in b number of bottles it 300 total bottles).

    a + b = 20 (total number of bottles.)

    Now use the substitution method to solve for a, the number of 12 ounce bottles:

    a + b = 20

    - a - a

    b = 20 - a (substitute 20 - a into the other equation for b)

    12a + 16 (20 - a) = 300 (Use distributive method

    12a + 320 - 16a = 300 (Combine a's and subtrace 320)

    - 320 - 320

    -4a = - 20 (Divide by - 4)

    a = 5

    There are 5 12 ounce bottles.
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