1. ## ratio box

PROBLEM: Use a ratio box to solve this problem. The ratio of winners to loosers was 7 to 5. If the total number of winners and loosers was 1260, how many more winners were there than loosers?

I don't necessarily want just an answer, I need to know how to set up this type of problem.
Thanks

2. ## Re: ratio box

Originally Posted by dylenjc
PROBLEM: Use a ratio box to solve this problem. The ratio of winners to loosers was 7 to 5. If the total number of winners and loosers was 1260, how many more winners were there than loosers?

I don't necessarily want just an answer, I need to know how to set up this type of problem.
Thanks
I don't know what is ratio box - however, I would use the following property of the ratios:

If

x/y = a/b

then

(x-y)/(x+y) = (a-b)/(a+b)

3. ## Re: ratio box

2 more winners per 12; 1260/12 = 105; 105 * 2 = 210

4. I could not find any useful information on "ratio box", so I'm not sure what that means, either.

Sometimes, Denis is too slick. Don't feel bad if you cannot understand his response; at first glance, I don't understand it either.

Subhotosh posted an algebraic relationship.

I realize that you did not post on one of the algebra boards, but algebra is the only tool I can come up with right now for this exercise.

If you could explain a "ratio box" example given to you, then maybe I could come up with something else.

Anyway, here is the algebraic solution. If you're not interested, feel free to ignore it.

You're looking for two numbers that add to make 1260 and divide to make 7/5.

Let the symbol W represent the number of winners.

Let the symbol L represent the number of losers.

The given information that "the ratio of winners to losers is 7/5" gives the following.

W/L = 7/5

The given information that "the total number of winners and losers is 1260" gives the following.

W + L = 1260

If we subtract the number of winners from 1260, then we get an expression for the number of losers written with the symbol W.

L = 1260 - W

We can replace the symbol L in the ratio with the expression 1260 - W.

W/L = 7/5

W/(1260 - W) = 7/5

When two fractions (ratios) are equal, we can "cross multiply".

W * 5 = 7 * (1260 - W)

We multiply the right-hand side using a rule called The Distributive Property.

5W = (7)(1260) - 7W

5W = 8820 - 7W

5W + 7W = 8820 - 7W + 7W

12W = 8820

Divide both sides by 12.

12W/12 = 8820/12

W = 735

The number of winners is 735.

1260 - 735 = 525

The number of losers is 525

CHECK THE RESULTS.

735/525 = 7/5

735 + 525 = 1260

It checks.

Again, if you understand little of what I typed because you have not seen algebra before, that's not your fault. Just ignore it. Perhaps, with the answers, you can work backwards to figure out your ratio-box method.

If not, then try to explain a ratio box example, and we'll go from there.

5. Hmmm, Denis might be on to something with that 105 that he typed.

I just realized that:

7 * 105 = 735

5 * 105 = 525

DENIS! Please explain the ratio box!

(Denis does not usually give away his "secrets" or explain his "methods", but I keep asking him anyway. Heh, heh.)

6. ## Re: ratio box

PROBLEM: Use a ratio box to solve this problem. The ratio of winners to loosers was 7 to 5. If the total number of winners and loosers was 1260, how many more winners were there than loosers?
where

W = # of Winners
L = # of Loosers

W/L = 7/5

(W-L)/(W+L) = (7-5)/(7+5)

W-L = 2/12 * 1260 = 210

7. ## Re: ratio box

Code:
*  *  *  *  *  *  *  *  *  *   *
*                              *
* 1260/12 = 105; 105 * 2 = 210 *
*                              *
*  *  *  *  *  *  *  *  *  *   *
Da Sir Denis Ratio Box.

8. ## Re: ratio box

Thanks for the help I think I may have it now,

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