Math

During its first week of business, a market sold a total of 108 apples and oranges. The second week, five times the number of apples and three times the number of oranges were sold. A total of 452 apples and oranges were sold during the second week. Determine how many apples and how many oranges were sold the first week.

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  1. a = apples

    o = oranges

    1 week :

    a + o = 108

    2 week :

    5 a + 3 o = 452

    Now you must solve system of 2 equations with 2 unknown :

    a + o = 108

    5 a + 3 o = 452

    The method of substitution:

    a + o = 108 Subtract o to both sides

    a + o - o = 108 - o

    a = 108 - o

    5 a + 3 o = 452

    5 * ( 108 - o ) + 3 o = 452

    5 * 108 - 5 * o + 3 o = 452

    540 - 5 o + 3 o = 452

    540 - 2 o = 452 Subtract 540 to both sides

    540 - 2 o - 540 = 452 - 540

    - 2 o = - 88 Divide both sides by - 2

    - 2 o / - 2 = - 88 / - 2

    o = 44

    a = 108 - o

    a = 108 - 44 = 64

    64 apples and 44 oranges

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