Question

5 of 5

Paul, Fiona and Pip share some sweets in the ratio 4:5:1. Paul gets 15 more sweets than Pip.
How many sweets does Fiona get?

Answer 1

Fiona gets 25 sweets

Explanation:

System of Equations

Paul, Fiona, and Pip have some sweets in the ratio 4:5:1. Let's call x,y, and z the number of sweets they have respectively.

The ratios can be written as three separate equations:

`(x)/(y)=(4)/(5)\qquad\qquad[1]`

`(y)/(z)=(5)/(1)\qquad\qquad[2]`

`(x)/(z)=(4)/(1)\qquad\qquad[3]`

Paul has 15 more sweets than Pip, then:

x = z + 15 [4]

Multiplying [3] by z:

x = 4z

Substituing in [4]

4z = z + 15

Subtracting z:

3z = 15

z = 15/3 = 5

Multiplying [2] by z:

y = 5z = 5*5 = 25

Fiona gets 25 sweets