SOLUTION: Two numbers are in ratio of 7:11. If 7 is added to each of the number, the ratio becomes 2:3. Find the numbers.

Question 516265: Two numbers are in ratio of 7:11. If 7 is added to each of the number, the ratio becomes 2:3. Find the numbers.
Found 2 solutions by Maths68, gc2000:
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Let x and y are two numbers

x:y=7:11
x/y=7/11
11x=7y
x=7y/11............(1)

(x+7):(y+7)=2:3
(x+7)/(y+7)=2/3
3(x+7)=2(y+7)
3x+21=2y+14
3x=2y+14-21
3x=2y-7............(2)
Put the value of x in (2) from (1)
3(7y/11)=2y-7
21y/11=2y-7
21y=11*(2y-7)
21y=22y-77
21y-22y=-77
-y=-77
y=77
Put the value of y in (1)
x=7y/11............(1)
x=7(77)/11
x=7*7
x=49

Numbers are 49 and 77

49/77=7/11=7:11
(49+7)/(77+7)=56/84=28/42=14/21=2/3=2:3
Answer by gc2000(22) (Show Source): You can put this solution on YOUR website!
Two numbers, x & y
given: x/y = 7/11 and
(x+7)/(y+7) = 2/3
cross multiply:
7y = 11x and
2(y+7) = 3(x+7)
2y + 14 = 3x + 21
substitute for 2y
(instead of isolating y, I will isolate 2y)
7y = 11x
times 2/7 both sides
2y = (22/7)x
substitute for 2y
2y + 14 = 3x + 21
(22/7)x + 14 = 3x + 21
subtract 14 and 3x both sides
(22/7)x - 3x = 7
(3 1/7)x - 3x = 7
(1/7)x = 7
multiply both sides by 7
x = 49

solve for y:
49/y = 7/11
y = 77

check
(49+7)/(77+7)
56/84
2/3
yes, this is the correct 2nd ratio.

x = 49, y = 77

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