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

Answer:

$Ratio =16 : 31$

Step-by-step 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

$\frac{x}{y} = \frac{1}{11}$ --- (1)

$\frac{x+17}{y+17} = \frac{2}{5}$ -- (2)

In (1), make y the subject

$\frac{x}{y} = \frac{1}{11}$

$y = 11x$

Substitute $y = 11x$ in (2)

$\frac{x+17}{y+17} = \frac{2}{5}$

$\frac{x+17}{11x+17} = \frac{2}{5}$

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

$Ratio =16 : 31$