Question

(Terms and Equations in Factual Problems) The Smith family consists of four people. Anna is three years older than Matthias. Miss Smith is four times as old as Anna. Mr Smith is five years older than his wife. Together they are 72 years. How old are the family members?

Answer 1

Given:

Anna is three years older than Matthias.

Miss Smith is four times as old as Anna.

Mr Smith is five years older than his wife.

Together they are 72 years.

To find:

The age of each family member.

Solution:

Let age of Matthias be x years.

Anna is three years older than Matthias.

Anna's age = x+3

Miss Smith is four times as old as Anna.

Miss Smith's age = 4(x+3)

Mr Smith is five years older than his wife Mrs Smith.

Mr Smith's age = 4(x+3)+5

Together they are 72 years.

`x+(x+3)+4(x+3)+[4(x+3)+5]=72`

`x+x+3+4x+12+4x+12+5=72`

`10x+32=72`

Subtract 32 from both sides.

`10x=72-32`

`10x=40`

Divide both sides by 10.

`x=4`

Now,

Matthias's age = 4 years

Anna's age = 4+3

= 7 years

Miss Smith's age = 4(4+3)

= 4(7)

= 28 years

Mr. Smith's age = 4(4+3)+ 5

= 28+5

= 33 years

Therefore, the ages of Matthias, Anna, Miss Smith and Mr Smith are 4, 7, 28 and 33 respectively.