Question

A brother and sister are comparing their ages. The older sister is 8 years less than twice the brother’s age. The sum of their ages is 25 years. Let "x" be the age of the brother. Set up and solve an equation for x.

Answer 1

The brother is 11 years and the sister 14 years

Explanation:

Let x represent the age of the brother and let y represent the age of the sister. Since the sum of their ages is 25 years, the sum can be represented by the equation:

x + y = 25 (1)

The sister age is 8 years less than twice the brother’s age, this can be represented by the equation:

y = 2x -8

2x - y = 8 (2)

Solve equation 1 and equation 2 simultaneously. Add equation 1 and equation 2, this gives:

3x = 33

x = 33/3

x = 11 years

Put x = 11 in equation 1:

11 + y = 25

y = 25 - 11

y = 14 years