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16 June, 03:52

Owen is making lemonade from concentrate. The number of quarts of water he needs is 4 times the number of quarts of concentrate. He wants to make 100 quarts of lemonade.

Let c represent the number of quarts of concentrate, and let w represent the number of quarts of water Owen will use. Which of the following systems of equations models this situation?

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  1. 16 June, 04:11
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    The system of equation that models the situation is:

    w = 4c

    w + c = 100

    And c = 20 quarts, 4c = 80 quarts and w = 80 quarts.

    Step-by-step explanation:

    1. Let's review the information given to us to answer the problem correctly:

    Owen wants to make 100 quarts of lemonade

    Number of quarts of water 4 times the number of quarts of concentrate

    2. Which of the following systems of equations models this situation?

    c = number of quarts of concentrate

    w = number of quarts of water

    Like the alternatives of systems of equations that model the situation were not given, let's write them by ourselves, this way:

    w = 4c (Number of quarts of water 4 times the number of quarts of concentrate)

    w + c = 100 (Owen wants to make 100 quarts of lemonade)

    Now, let's solve for c and w, this way:

    w = 100 - c

    Substituting w in the first equation, we have:

    100 - c = 4c

    100 = 5c

    c = 20 ⇒ 4c = 20 * 4 = 80

    w = 4 * 20

    w = 80

    The system of equation that models the situation is:

    w = 4c

    w + c = 100

    And c = 20 quarts, 4c = 80 quarts and w = 80 quarts.
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