Ratio and Proportion Word Problem *So Confused*

[A Kid Called Matthew]

The Problem: Revenue from a state lottery is divided between education and administrative costs in the ratio of 4 to 3. If the lottery revenue this year is $24,000,000 how much money will go to education?

Now this is how I set the problem up. x = money towards education

4 = x
3 24, 000, 000

3x = 72,000,000/3
3

x = 24,000,000

But this is the wrong answer. So I don't know how to apply the correct thinking towards this problem nor know how to set it the correct equation in order to solve it.

Please help! Much appreciated!

- Matthew

 

[rbcc]

I'm not sure but this is how I would do it

4/3=education/administration
let e represent the amount of money allocated to education
let a represent the amount of money allocated to administration
4/3=e/a
4a=3e

and
a+e=24 because the total revenue is 24 million

To solve (the answer is in millions) use substitution
e=24-a
4a=3(24-a)
4a=72-3a
7a=72
a=10.28571429

e=24-a=24-10.28571429=13.71428571

 

[Mrspi]

The Problem: Revenue from a state lottery is divided between education and administrative costs in the ratio of 4 to 3. If the lottery revenue this year is $24,000,000 how much money will go to education?

Now this is how I set the problem up. x = money towards education

4 = x
3 24, 000, 000

3x = 72,000,000/3
3

x = 24,000,000

But this is the wrong answer. So I don't know how to apply the correct thinking towards this problem nor know how to set it the correct equation in order to solve it.

Please help! Much appreciated!

- Matthew

Here's how I would think about it. A ratio of 4:3 means that the 4 parts of the fund go to education, and 3 parts go to administrative costs. The entire fund, then, consists of 4 parts + 3 parts, or 7 parts.

Since 4 of the 7 parts go to education, we could say that 4/7 of the fund is devoted to education; since 3 of the 7 parts go to administrative costs, we could say that 3/7 of the fund is for administrative costs.

Note that 4/7 + 3/7 = 7/7, or 1, or the "whole fund".

Ok...

We know the amount in the fund is $24,000,000. How much goes to education? We could solve this a couple of ways. Let x = amount that goes to education

Using a proportion, 4/7 = x/24000000

Or, we know that 4/7 of the total is for education, so (4/7)*24000000 = x