The ratio of two numbers is 4:5.After Adding 20 to the smaller number and subtracting 20 From the greater number the ratio becimes 14:13 .Find the numbers.

Hey there! I'll try to provide you with my best answer.

x = 120 and y = 150

(x / y) = (4 / 5)    

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  (proof):  

120 / 150 = 12 / 15 = 4 / 5  

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

the answer is b