# Answer to Question #31932 in Algebra for vishnupriya

Question #31932

Two numbers are such that the ratio between them is 3:5. If each is increased by 10, the ratio

between the new numbers so formed is 5:7. Find the original numbers.

between the new numbers so formed is 5:7. Find the original numbers.

Expert's answer

Let the first number is x, the second is y.Then x/y=3/5 , 3y=5x

On the other hand (x+10)/(y+10)=5/7 whence 7(x+10)=5(y+10) .

We get that 3y=5x, 7x+70=5y+50

3y=5x, 5y=7x+20

y=5x/3, y=(7x+20)/5

Then we can find x

5x/3=(7x+20)/5

25x=3(7x+20)

25x=21x+60

4x=60

x=15

Then y=5x/3=5*15/3=25

x=15, y=25

On the other hand (x+10)/(y+10)=5/7 whence 7(x+10)=5(y+10) .

We get that 3y=5x, 7x+70=5y+50

3y=5x, 5y=7x+20

y=5x/3, y=(7x+20)/5

Then we can find x

5x/3=(7x+20)/5

25x=3(7x+20)

25x=21x+60

4x=60

x=15

Then y=5x/3=5*15/3=25

x=15, y=25

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