Question

John’s father is 5 times older than John and John is twice as old as his sister Alice. In two years time, the sum of their ages will be 58. How old is John

Answer 1

John’s age is 8 years

Explanation:

Let

x -----> John’s father's age

y -----> John’s age

z -----> John’s sister's age

we know that

`x=5y` -----> equation A

`y=2z`

`z=y/2` -----> equation B

`(x+2)+(y+2)+(z+2)=58`

`x+y+z+6=58`

`x+y+z=52` -----> equation C

Substitute equation A and equation B in equation C and solve for y

`5y+y+y/2=52`

Multiply by 2 both sides to remove the fraction

`10y+2y+y=104`

`13y=104`

`y=8`

Find the value of x

`x=5(8)=40`

Find the value of z

`z=8/2=4`

therefore

John’s father's age is 40 years

John’s age is 8 years

John’s sister's age is 4 years