Question

Ralf and Susie share $57 in the ratio 2 : 1. (a) Calculate the amount Ralf receives (b) Ralf gives $2 toSusie. Calculate the new ratio Ralf’s money : Susie’s money. Give your answer in its simplest form.

Answer 1

Given:

Ralf and Susie share $57 in the ratio 2 : 1.

To find:

(a) Calculate the amount Ralf receives

(b) Ralf gives $2 to Susie. Calculate the new ratio of Ralf’s money : Susie’s money.

Solution:

(a). Finding the share of Ralf:

Total amount = $ 57

The ratio of the share of Ralf and Susie = 2:1

∴ Ralf's share of money = $\frac{2}{2+1} \times 57 = \frac{2}{3} \times 57 = 2 \times 19 = 38$

and

∴ Susie's share of money = $\frac{1}{2+1} \times 57 = \frac{1}{3} \times 57 = 19$

Thus, the amount Ralf receives is → $ 38

(b). Finding the new ratio:

After Ralf gives $ 2 to Susie,

Amount left with Ralf = 38 - 2 = $ 36

Amount with Susie = 19 + 2 = $ 21

∴ The new ratio of share is,

= $\frac{Ralf's \:money}{Susie's \:money}$

= $\frac{36}{21}$

on dividing both numerator and denominator by 3, we get

= $\bold{ \frac{12}{7} }$

Thus, the new ratio Ralf’s money:Susie’s money is → 12:7.

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Answer 2

Given:

Ralf and Susie share $57 in the ratio 2 : 1.

To find:

(a) Calculate the amount Ralf receives

(b) Ralf gives $2 to Susie. Calculate the new ratio of Ralf’s money : Susie’s money.

Solution:

(a). Finding the share of Ralf:

Total amount = $ 57

The ratio of the share of Ralf and Susie = 2:1

∴ Ralf's share of money = $\frac{2}{2+1} \times 57 = \frac{2}{3} \times 57 = 2 \times 19 = 38$

and

∴ Susie's share of money = $\frac{1}{2+1} \times 57 = \frac{1}{3} \times 57 = 19$

Thus, the amount Ralf receives is → $ 38

(b). Finding the new ratio:

After Ralf gives $ 2 to Susie,

Amount left with Ralf = 38 - 2 = $ 36

Amount with Susie = 19 + 2 = $ 21

∴ The new ratio of share is,

= $\frac{Ralf's \:money}{Susie's \:money}$

= $\frac{36}{21}$

on dividing both numerator and denominator by 3, we get

= $\bold{ \frac{12}{7} }$

Thus, the new ratio Ralf’s money:Susie’s money is → 12:7.

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