Question

siw is a fourth as old as mother, and Mona is a fifth as old as mother. Mother is 22 years older than the two girls together. How old are they?

Answer 1

Siw's age is 10 years old

Mona's age is 8 yers old

Mother's age is 40 years old

Explanation:

Let

x ----> Siw's age

y ---> Mona's age

z ---> Mother's age

we know that

Siw is a fourth as old as mother

so

`x=(1)/(4)z` ----> equation A

Mona is a fifth as old as mother

so

`y=(1)/(5)z` ----> equation B

Mother is 22 years older than the two girls together.

so

`z=x+y+22` ----> equation C

substitute equation A and equation B in equation C

`z=(1)/(4)z+(1)/(5)z+22`

solve for z

Multiply by 20 both sides to remove the fraction

`20z=5z+4z+440`

`20z-9z=440\\11z=440\\z=40\ years`

Find the value of x

`x=(1)/(4)(40)=10\ years`

Find the value of y

`y=(1)/(5)(40)=8\ years`

therefore

Siw's age is 10 years old

Mona's age is 8 yers old

Mother's age is 40 years old