Illustrating Word Problems

[SCSmith]

I am doing a self study of word problems for Algebra 1. In the classroom the instructor uses tables to illustrate certain problems. If I need a visual illustration how do I go about showing what I have done in a table (say for a mixture problem or what have you?)

 

[Denis]

An example would be "appreciated"....

 

[soroban]

Hello, SCSmith!

We have 60 liters of solution which is 10% salt.
. . We have a second solution which is 20% salt.
How much of the second solution must be added to get a solution which is 14% salt?

Obviously, we are concerned with the concentration of salt.
. . And that is the basis for our table.

We use the formula: .[Amount of solution] x [% of salt] .= .[amount of salt]
. This is written across the top of the table.

We have two solutions to combine to get a third mixture.
. . Those are the rows of the table.

                Amt.  x  %  =     Salt
    ---------+--------+-----+--------------+
      Soln 1 |        |     |              |
    ---------+--------+-----+--------------+
      Soln 2 |        |     |              |
    ---------+--------+-----+--------------+
     Mixture |        |     |              |
. . ---------+--------+-----+--------------+

We can fill in the Percent column.
. . Solution 1 is 10% salt.
. . Solution 2 is 20% salt.
. . The mixture will be 14% salt.

                Amt.  x  %  =     Salt
    ---------+--------+-----+--------------+
      Soln 1 |        | 10% |              |
    ---------+--------+-----+--------------+
      Soln 2 |        | 20% |              |
    ---------+--------+-----+--------------+
     Mixture |        | 14% |              |
. . ---------+--------+-----+--------------+

We can fill in the Amount column.
. . Solution 1 has 60 liters of liquid.
. . We will add x liters of 20% solution.
. . The mixture will have x + 60 liters of liquid.

                Amt.  x  %  =     Salt
    ---------+--------+-----+--------------+
      Soln 1 |   60   | 10% |              |
    ---------+--------+-----+--------------+
      Soln 2 |    x   | 20% |              |
    ---------+--------+-----+--------------+
     Mixture | x + 60 | 14% |              |
. . ---------+--------+-----+--------------+

We use the formula to fill in the last column.
. . Solution 1: .60 liters of 10% salt: .\(\displaystyle 60 \times 10\% = 6\) liters of salt.
. . Solution 2: .x liters of 20% salt: .\(\displaystyle 0.20x\) liters of salt.
. . Mixture: .x + 60 liters of 14% salt: .\(\displaystyle 0.14(x + 60)\) liters of salt.

                Amt.  x  %  =     Salt
    ---------+--------+-----+--------------+
      Soln 1 |   60   | 10% |       6      |
    ---------+--------+-----+--------------+
      Soln 2 |    x   | 20% |     0.20x    |
    ---------+--------+-----+--------------+
     Mixture | x + 60 | 14% | 0.14(x + 60) |
    ---------+--------+-----+--------------+

Our equation comes from the third column:

. . [Salt in solution 1] + [salt in solution 2] .= .[salt in mixture]
. . . . . . . . . . . 6 . . . . .+ . . . . . 0.2x . . . . . . = . . 0.14(x + 60)

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

This can be modified to work for almost any word problem:
. . distance, investment, work, age, etc.

 

[stapel]

I am doing a self study of word problems...how do I go about showing what I have done...?

That will, to some extent, depend upon the specifics of the exercise.

There are entire books written on the topic of "algebra word problems", which we obviously can't reproduce here. If you have a specific exercise in mind, please reply with that information. But if you are, as you appear to be, asking for general guidelines, one of those books might be more appropriate.

Your local library and/or book retailer should have a variety of books from which to choose.

Eliz.