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18 February, 16:06

The sum of two numbers is 15. Four times one of the numbers is twelve more than two times the other number. What are the two numbers?

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  1. 18 February, 17:03
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    Let a and b be our two numbers.

    Here is the set up:

    a + b = 15 ... A

    4a = 2b + 12 ... B

    We have a system of equations in two variables.

    Solve equation A for either a or b. I decided to solve for a.

    a + b = 15

    a = 15 - b

    Plug into equation B.

    4 (15 - b) = 2b + 12

    Solve for b.

    60 - 4b = 2b + 12

    -4b - 2b = 12 - 60

    -6b = - 12

    b = - 12/-6

    b = 2

    We now know that b is 2. To find a, plug b = 2 into either equation A or B.

    As you can see, equation A is easier to deal with.

    a + b = 15

    a + 2 = 15

    a = 15 - 2

    a = 13

    The two missing numbers are 2 and 13.
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