Ratio Set-Up Problem

Date: 09/02/2003 at 23:15:08
From: Vanessa
Subject: how to solve ratio problems

Here is an example of a problem that I don't know how to set up:
Concrete can be made by mixing cement, sand, and gravel in the ratio
3:6:8. How much gravel is needed to make 850 cubic meters of concrete?

Date: 09/03/2003 at 15:28:57
From: Doctor George
Subject: Re: how  to solve ratio problems

Hi Vanessa,

Thanks for writing to Doctor Math.

We could think of this problem as having three variables, but with a 
little trick we can write it with just one. Let's define the amounts 
of material like this.

     cement = 3x
     sand   = 6x
     gravel = 8x

We don't know x yet, but can you see that the ratios are correct? 
The next step is to find x with this equation.

     3x + 6x + 8x = 850

We can now solve for x, and then compute 8x to get the amount of 
gravel.

Does that make sense? Write again if you need more help.

- Doctor George, The Math Forum
  http://mathforum.org/dr.math/