SOLUTION: 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.

Question 1062383: 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.

Found 3 solutions by josgarithmetic, ankor@dixie-net.com, rothauserc:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
The ratios are 4/5 and 14/13.

Original ratio can be .

Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
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.
:
let x = the multiplier
then
4x = the 1st number
and
5x = the 2nd number
:
"After adding 20 to the smaller number and subtracting 20 from the greater number the ratio becomes 14:13."
=
Cross multiply
14(5x-20) = 13(4x+20)
70x - 280 = 52x + 260
70x - 52x = 260 + 280
18x = 540
x = 540/18
x = 30 is the multipliers
:
Find the the numbers
4(30) = 120 is the first number
and
5(30) = 150 Is the 2nd number

Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
(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
:
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x = 120 and y = 150
:
check answers
:
120 / 150 = 12 / 15 = 4 / 5
:
(120+20) / (150-20) = 140 / 130 = 14 / 13
:
answers check
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