Ratio prob: If ratio of 2x to 5y is 3 to 4, what is ratio of

If the ratio of 2x to 5y is 3 to 4, what is the ratio of x to y?

I can see the answer is 15 to 8, I am just unable to set the problem up and explain to my son. Please help. Thank you.

Re: Ratio problem beginning Algebra

If the ratio of 2x to 5y is 3 to 4, what is the ratio of x to y?
\(\displaystyle \frac{2x}{5y}=\frac{3}{4}\)
Just work with this equation and get x over y on the right side all by itself. For instance, if you multiply both sides of the equation by 5, the denominator on the left side will be y all by itself. Get the idea?

A ratio can be written as (say we're talking about dogs and cats), "the ratio of dogs to cats is 5 to 6", or "dogs:cats is 5:6". But you can also write it like:

dogs/cats = 5/6

(as a fraction)

So when they ask for the ratio of x to y, or the ratio x:y, they are asking for:

x/y = ?


You already know the ratio of 2x:5y is equal to 3:4 or:

(2x)/(5y) = 3/4

Now you just have to (as Loren said) work the equation to get (x/y) by itself on one side. Having said that:


(2x)/(5/y) = 3/4 >>>>>>>>>>>>> (2x)/(5/y) = (2/5)*(x/y)

(2/5)(x/y) = 3/4

Multiply the left side by the reciprocal of (2/5) to get rid of (2/5) - but don't forget to do the same thing on the right side:
(5/2)*(2/5)(x/y) = (3/4)*(5/2) >>>>>>>>>>>>>(5/2)*(2/5) = 1, (3/4)*(5/2) = 15/8


(1)*(x/y) = 15/8
x/y = 15/8

or

x:y = 15:8

or

x to y = 15 to 8

Get it?

http://tinyurl.com/6kwmp5

Thanks!