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29 October, 12:08

The sum of 3 numbers is 15. two times the smallest is 1 less than the largest, while the sum of the largest and smallest is 10. use a linear system in three variables to find the three numbers.

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  1. 29 October, 15:35
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    Let x = smallest number

    y = middle number

    z = largest number

    Equations:

    sum of 3 numbers: x + y + z = 15

    two times smallest is 1 less than largest: 2x = z - 1

    sum of largest and smallest is 10: z + x = 10

    z + x = 10 can be solved for z ⇒ z = 10 - x

    substitute into 2x = z - 1 ⇒ 2x = 10 - x - 1

    3x = 9

    x = 3 (divided both sides of equation by 3)

    Since z + x = 10 ⇒ z + 3 = 10 ⇒ z = 7

    Substitute values for x and z into x + y + z = 15 ⇒ 3 + y + 7 = 15

    y + 10 = 15

    y = 5

    answer: 3, 5, 7
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