Solve please thanks

Question

Natasha and Richard win some money and share it in the ratio 5:1. Natasha gets £32 more than Richard. How much did Richard get?

Answer 1

Hi Iz,

We need to set up two equations to relate how much money Natasha wins in comparison to richard. Right now we don't know how much either of them wins. Let the variable N be the money that Natasha wins, and R be the money that Richard wins.

From the problem we know that Natasha gets 5 times as much money as Richard (5:1 ratio). So our first equation will be:

N = 5R

We also know that Natasha makes £32 more than Richard, so our second equation will be:

N = R + 32

Now, we have two equations and two unknowns, so we can solve them! Since N = 5R and also N = R + 32, we can say that:

5R = R + 32

Subtracting R from both sides,

4R = 32

This means that R = 8, so Richard makes £8!