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

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