Eight years ago, the daughters age was thrice the son’s age. Now the daughter’s age is 4 years more than the son’s age. Find their present a

Question

Eight years ago, the daughters age was thrice the son’s age. Now the daughter’s age is 4 years more than the son’s age. Find their present ages.​

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Ben Gia 5 years 2021-07-18T09:57:54+00:00 1 Answers 480 views 0

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  1. trucchi
    -2
    2021-07-18T09:59:23+00:00
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    Answer:

    Let s be the son’s current age and d be the daughter’s current age. The system of equations is:

    s – 10 = 2(d – 10)

    s = 3 + d

    Since s is already set to an equation, we can use the substitution method for s in the other equation:

    s = 3 + d

    s – 10 = 2(d – 10)

    3 + d – 10 = 2(d – 10)

    Simplify and solve for d:

    3 + d – 10 = 2(d – 10)

    -7 + d = 2d – 20

    -7 = d – 20

    13 = d

    The daughter is 13 years old. To solve for the son’s age, we will plug in the solution for d into one of the equations. The second one is simpler so we will use that:

    s = 3 + d

    s = 3 + 13

    s = 16

    The son is 16 years old. Let us use the other equation to check our solutions:

    s – 10 = 2(d – 10)

    16 – 10 = 2(13 – 10)

    6 = 2(3)

    6 = 6

    It checks out. The son is 16 years old, and the daughter is 13 years old.

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