The prices of two ratios 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

4:1

Step-by-step explanation:

x+20 : y+20 = 5 : 2

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

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

2x+40 = 5y+100

2x = 5y+60 (1)

x-5 : y-5 = 5:1

(x-5) / (y-5) = 5/1

x-5 = 5 (y-5)

x-5 = 5y-25

x = 5y-20 (2)

Solve (1) & (2) simultaneously,

2 (5y-20) = 5y+60

10y-40 = 5y+60

5y = 100

y = 20

x = 5y-20

x = 5 (20) - 20 = 100-20

x = 80

x:y

80:20

4:1

Answer: x:y = 2:5

Step-by-step explanation:

Given : The prices of two radios are in the ratio x:y

When the prices are both increased by £20, the ratio becomes 5:2

Then,

When the prices are both reduced by £5, the ratio becomes 5:1

Then,

Subtract (2) from (1), we get

Put this value in (2), we get

Now, the ratio of x:y=

Dividing 4 from both the numerator and denominator, we get

x:y = = 2:5

Credit: JeanaShupp