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

4:1

Explanation:

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

2x + 40 = 5y + 100

2x - 5y = 60

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

x - 5 = 5y - 25

x - 5y = -20

x = 80 (solve the two equations simultaneously)

80 - 5y = -20

5y = 100

y = 20

x:y = 80:20

x:y = 4:1

Answer 2

x : y = 4 : 1

Explanation:

(x+20) : (y+20) = 5 : 2 and (x-5) : (y-5) = 5 : 1

When we multiply the outer and inner members we get:

2x+40 = 5y+100 and x-5 = 5y-25

When we arrange the both equations we get:

2x-5y = 60 and x-5y = -20

When we subtract second equation from the first we get:

x = 80 Now we will replace x=80 in the second equation and get:

80-5y = -20 => -5y= -20-80 => -5y= - 100

Now we will multiply the both sides with number (-1) and get:

5y= 100 => y= 100/5 = 20 => y=20

x : y = 80 : 20 => x : y = 4 : 1

God with you!!!