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### Ali has £4. Ben has twice as much as Ali. Ben has two-thirds of the amount Cara has. The amount Cara has is four-fifths of her age in years. How old is Cara?

We know Ben has double what Ali has, so we can immediately work out that Ben has £8, because:

4 x 2 = 8.

We will now call the amount Cara has c. The amount Ben has (£8, as shown above) is two-thirds of what Cara has, so 2/3 of c is 8. To work out how much Cara has, we rearrange the following equation to get c:

2/3 x = 8

First multiply both sides by 3:

2 x c = 24

And divide both sides by 2:

c = 12

Finally, we need to work out Cara's age, which we will call d. The amount she has (£12, as we just worked out) is four-fifths of her age in years, so 4/5 of is 12. In a similar way to before, we rearrange the following equation:

4/5 x = 12

Multiply both sides by 5:

4 x = 60

And divide both sides by 4:

= 15.

And that's our answer! Cara is 15 years old.

2 years ago

Answered by Pippa, a GCSE Maths tutor with MyTutor

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