Question

.On 1st March 2001, the ratio of Freddie’s age to his mother’s age was 1:11

On 1st March 2018, the ratio of Freddie’s age to his mother’s age was 2:5
Write the ratio of Freddie’s age to his mother’s age on 1st March 2030

Answer 1

`Ratio =16 : 31`

Explanation:

Let

x = Freddie's age and y = His mother's age

Given

2001:=
`x : y = 1 : 11`

2018:=
`x +17: y + 17= 2 : 5`

Required

The ratio of their age in 2030

`x : y = 1 : 11`

`x +17: y + 17= 2 : 5`

Express as fractions

`(x)/(y) = (1)/(11)` --- (1)

`(x+17)/(y+17) = (2)/(5)` -- (2)

In (1), make y the subject

`(x)/(y) = (1)/(11)`

`y = 11x`

Substitute
`y = 11x` in (2)

`(x+17)/(y+17) = (2)/(5)`

`(x+17)/(11x+17) = (2)/(5)`

Cross Multiply

`5(x +17) = 2(11x + 17)`

`5x +85 = 22x + 34`

Collect like terms

`22x - 5x = 85 - 34`

`17x = 51`

`x =3`

`y = 11x`

`y = 11*3`

`y = 33`

This means that: In 2001, Freddie was 3 and his mother was 33

In 2030 (29 years after);

Freddie will be: 3 + 29 = 32

His mother will be: 33 + 29 = 62

So, the ratio is:

`Ratio =32 : 62`

Divide by 2

`Ratio =16 : 31`