SOLUTION: Two numbers are such that the ratio between them is 3:5. If each is increased by 10, the ratio b/w the new numbers so formed as 5:7. Find the original number?

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Two numbers are such that the ratio between them is 3:5. If each is increased by 10, the ratio b/w the new numbers so formed as 5:7. Find the original number?      Log On


   

Question 981211: Two numbers are such that the ratio between them is 3:5. If each is increased by 10, the ratio b/w the new numbers so formed as 5:7. Find the original number?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Numbers x and y.

system%28x%2Fy=3%2F5%2C%28x%2B10%29%2F%28y%2B10%29=5%2F7%29

7%28x%2B10%29=5%28y%2B10%29
7x%2B70=5y%2B50
7x%2B5y=-20
-
5x=3y
y=5x%2F3
-
7x%2B5%285x%2F3%29=-20
21x%2B25x=-60
46x=-60
23x=-30
highlight%28x=-30%2F23%29
-
Find y using the found x.
y=5%28-30%2F23%29%2F3
y=-150%2F%2823%2A3%29
highlight%28y=-50%2F23%29

CHECK:
The first ratio for x and y check perfectly.
-
The plus-ten ratio,
%28-30%2F23%2B10%29%2F%28-50%2F23%2B10%29-----------do the arithmetic. How is it?

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Two numbers are such that the ratio between them is 3:5. If each is increased by 10, the ratio b/w the new numbers so formed as 5:7. Find the original number?
Let multiplicative factor be x

Then numbers are: 3x and 5x

We then get: %283x+%2B+10%29%2F%285x+%2B+10%29+=+5%2F7

7(3x + 10) = 5(5x + 10) -------- Cross-multiplying

21x + 70 = 25x + 50

21x - 25x = 50 - 70 

- 4x = - 20

x+=+%28-+20%29%2F%28-+4%29, or 5

Smaller original number:  3(5), or highlight_green%2815%29

Larger original number:   5(5), or highlight_green%2825%29