If you add Natalie’s age and Fred’s age, the result is 40. If you add Fred’s age to 4 timesNatalie’s age, the result is 76. Write and solve

Question

If you add Natalie’s age and Fred’s age, the result is 40. If you add Fred’s age to 4 timesNatalie’s age, the result is 76. Write and solve a system of equations to find how old Fred and Natalie are.

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Delwyn 2 months 2021-07-31T05:52:55+00:00 1 Answers 3 views 0

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    2021-07-31T05:54:51+00:00

    Answer:

    Natalie is 12 years and Fred is 28 years

    Step-by-step explanation:

    lets assume Natalie’s age is X and Fred’s age is Y

    From the first sentence: X+Y = 40

    From the second sentence: Y + 4X = 76

    lets rearrange the equations

    X+Y =40 ……. equation 1

    4X+Y=76…….. equation 2

    To solve both equations, we will have to look for a way to eliminate one of the unknown to leave us with one unknown. since there are two +Y in both equations, we can subtract both equations to eliminate Y. Please note that whatever you do to one of the unknown in this equations applies to all other numbers & alphabets

    So: 1. X – 4X = -3X

    2. Y – Y = 0

    3. 40 -76 = -36

    writing the equation as one will be -3X = -36

    X = 12

    Put X = 12 into any of the equation

    By putting X as 12 into equation 1 : 12 + Y = 40

    Y = 40 -12 =28

    Recall that Natalie is X and Fred is Y

    Therefore Natalie is 12 years and Fred is 28 years

    be

    To crosscheck put in the gotten answers into the equations

    X+Y =40 .…… 12 + 28 = 40

    4X+Y=76…….. 4(12) + 28 = 76

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