Question

The prices of two radios are in the ratio x: y When the prices are both increased by £20, the ratio becomes 5:2 When the prices are both reduced by £5, the ratio becomes 5:1 Express the ratio x: y in its lowest terms.

Answer 1

(x + 20)/(y + 20) = 5/2

(x - 5)/(y - 5) = 5

2(x + 20) = 5(y + 20)

2x + 40 = 5y + 100

2x - 5y = 60

x - 5 = 5(y - 5)

x - 5 = 5y - 25

x - 5y = -20

2x - 5y = 60

x - 5y = -20

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x = £80, y = £20

x:y = £80:£20 = 4:1 = 4