Distance=Rate*Time Help          

  To solve mixture weighted average problems, it is best to use a 3 x 3 table. A table can be used for distance problems as well. (For more on distance problems click here.)  The Amounts will be the first column, the Percentage will be the middle column, and Total will be the last column.  You will find the values for the Total column by multiplying the first two columns.  The top row will be Have (how much you start with), the middle row is Add (how much you are adding), and the bottom row is Get (what you will get after you add to what you have).  You will find the Get row by adding the above two rows (except the percent column).

For example:  If Tom has 3 gallons of  60% orange juice, how many gallons of pure (100%) orange juice should he add to obtain a mixture of 75% orange juice?

The box should be set up as follows:

(Notice: The percents change to decimals when you multiply.)

            In this table we see that the product of the first two columns equals the third column, and we see that in the first column and the third column the first two entries are added to get the bottom row.  As a result the equation looks like this:

3(.60) + 1x = .75(x+3)
1.8 + 1x     = .75x + 2.25   Simplify and distribute
.25x = .45                Subtract .75x and 1.8 from both sides
x = 1.8                Divide both sides by .25