Thread: Ratio

The sum of two numbers is five times the difference of the numbers. What is the ratio of the largest to the smaller?

The answer is 3:2, but I don't know what to do in order to get that. Thanks to anyone who can help.

Originally Posted by Averee

The sum of two numbers is five times the difference of the numbers. What is the ratio of the largest to the smaller?

The answer is 3:2, but I don't know what to do in order to get that. Thanks to anyone who can help.

Hi,

let x be the greater number and
y the smaller.

Then you know:

x + y = 5(x - y)

x + y = 5x - 5y
6y = 4x Now divide by y(the samller number) and by 4

Code:

 6     x
--- = ---
 4     y

You can simplify the LHS of the equation and you'll get the given result.

EB

Thank you, but how did you get 6y to equal 4x?

Originally Posted by Averee

Thank you, but how did you get 6y to equal 4x?

we had x + y = 5x - 5y (do you understand how he got to that?)

so x + y = 5x - 5y, add 5y to both sides we get

x + y + 5y = 5x, now subtract x from both sides, we get

y + 5y = 5x - x, now combine the x's and y's

6y = 4x

Ah, thank you. I guess I kept subtracting x and y and getting 4x - 6y = 0. Thanks.

Originally Posted by Averee

Ah, thank you. I guess I kept subtracting x and y and getting 4x - 6y = 0. Thanks.

but that's the same thing as well

4x - 6y = 0, add 6y to both sides, we get

4x = 6y

I see. I guess I just keep confusing myself, lol. Thanks again.