Increasing/Decreasing by a Percent - 12

Increasing/Decreasing by a Percent - 12

Mixture problems involve mixing two different concentrations to obtain some concentration in between. Often these problems are stated as alcohol or acid solutions, but there are many more types. For example, you might want to know how many pure peanuts should be mixed with a 40% peanut mixture to obtain a 50% peanut mixture. You might have a two-cycle engine requiring a particular oil and gas mixture. Or, you might have a recipe calling for 1% fat milk and all you have on hand is 2% fat milk and 1 2% fat milk. These problems can be solved using the method illustrated below.

Increasing/Decreasing by a Percent - 11

Increasing/Decreasing by a Percent - 11

Some money problems involve one quantity divided into two investments paying different interest rates. Such questions are phrased ‘‘How much was invested at ___%?’’ or ‘‘How much was invested at each rate?’’

Increasing/Decreasing by a Percent - 10

Increasing/Decreasing by a Percent - 10

Coin problems are also common algebra applications. Usually the total number of coins is given as well as the total dollar value. The question is normally ‘‘How many of each coin is there?’’

   Let x represent the number of one specific coin and put the number of other coins in terms of x. The steps involved are:

Increasing/Decreasing by a Percent - 9

Increasing/Decreasing by a Percent - 9

Grade computation problems are probably the most useful to students. In these problems, the formula for the course grade and all but one grade are 224 given. The student is asked to compute the unknown grade in order to ensure a particular course average.

Increasing/Decreasing by a Percent - 9

Increasing/Decreasing by a Percent - 9

The smaller number is 4 and the larger is 11 – x == 11 – 4 = 7.

   Algebra students are often asked to compute people’s ages. The steps I solving such problems are usually the same as those used above.