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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?

Sagot :

elcharly64

Answer:

Fiona gets 25 sweets

Step-by-step 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:

[tex]\frac{x}{y}=\frac{4}{5}\qquad\qquad[1][/tex]

[tex]\frac{y}{z}=\frac{5}{1}\qquad\qquad[2][/tex]

[tex]\frac{x}{z}=\frac{4}{1}\qquad\qquad[3][/tex]

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

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