Question

The ratio of two numbers is 4:5. After adding 20 to the smaller number and subtracting 20 from the greater number the ratio becomes 14:13. Find the numbers​

Answer 1

(x / y) = (4 / 5)

:

cross multiply fractions

:

1) 5x = 4y

:

( (x + 20 ) / (y - 20) ) = (14 / 13)

:

cross multiply fractions

:

13(x + 20) = 14(y - 20)

:

13x + 260 = 14y - 280

:

2) 13x - 14y = -540

:

solve equation 1) for x

:

x = 4y/5

:

now substitute for x in equation 2)

:

13(4y/5) - 14y = -540

:

multiply both sides of = by 5

:

52y - 70y = -2700

:

-18y = -2700

:

y = 150

:

x = 4(150) / 5 = 120

:

*************************************************

x = 120 and y = 150

:

check answers

:

120 / 150 = 12 / 15 = 4 / 5

:

(120+20) / (150-20) = 140 / 130 = 14 / 13

I HOPE YOU UNDERSTAND... :)

HAPPY LEARNING... :)