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

Answer:

Siw's age is 10 years old

Mona's age is 8 yers old

Mother's age is 40 years old

Step-by-step 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

$x=\frac{1}{4}z$ ----> equation A

Mona is a fifth as old as mother

so

$y=\frac{1}{5}z$ ----> 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

$z=\frac{1}{4}z+\frac{1}{5}z+22$

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

$x=\frac{1}{4}(40)=10\ years$

Find the value of y

$y=\frac{1}{5}(40)=8\ years$

therefore

Siw's age is 10 years old

Mona's age is 8 yers old

Mother's age is 40 years old