A family has three children.The oldest is 4 years older than the middle,and the youngest child is 2 years younger than the middle child.The

Question

A family has three children.The oldest is 4 years older than the middle,and the youngest child is 2 years younger than the middle child.The sum of the ages of the children is 26.

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Hưng Khoa 4 months 2021-08-22T11:15:49+00:00 1 Answers 1 views 0

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    2021-08-22T11:17:13+00:00

    Answer:

    The age of the youngest child = x = 6 years

    The age of middle child = y = 8 years

    The age of the oldest child = z = 12 years

    Step-by-step explanation:

    Let us represent:

    The age of the youngest child = x

    The age of middle child = y

    The age of the oldest child = z

    The sum of the ages of the children is 26.

    Hence: x + y + z = 26…… Equation 1

    The oldest is 4 years older than the middle

    z = 4 + y

    The youngest child is 2 years younger than the middle child

    x = y – 2

    Hence, we substitute 4 + y for z and y – 2 for x in Equation 1

    x + y + z = 26…… Equation 1

    y – 2 + y + 4 + y = 26

    y + y + y -2 +4 = 26

    3y + 2 = 26

    Subtract 2 from both sides

    3y + 2 – 2 = 26 – 2

    3y = 26 – 2

    3y = 24

    y = 24/3

    y = 8

    Solving for x

    x = y – 2

    x = 8 – 2

    x = 6

    Solving for z

    z = 4 + y

    z = 4 + 8

    z = 12

    Therefore:

    The age of the youngest child = x = 6 years

    The age of middle child = y = 8 years

    The age of the oldest child = z = 12 years

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