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Percent Problems The word percent comes from Latin and literally means divide (per) by 100 (cent). Even the % symbol, if you look closely at it, resembles /100 . Thus, percents are just another way of writing fractions or decimal fractions. In the chart below are shown the conversions between fractions, decimals, and percents. A more detailed discussion for converting fractions into decimals and decimals into fractions was provided in Unit 3. As examples consider the following : As an application of these methods consider the following problem. The reduction percentage for automotive paint is the amount (volume) of thinner added divided by the amount (volume) of paint originally present. For a 150% reduction how many gallons of thinner must be added to 7.5 gallons of paint? The solution is that There are three basic percent problems. 1. Missing part. 2. Missing total amount. 3. Missing percent. All three types of problems can be solved by the same strategy of translating word problems into math and a “little bit” of algebra. The translation is as follows : what means (an unknown, often called x ) is means = of means (multiplication) The “little bit” of algebra is as follows. Suppose you wanted to know from the fact that The “obvious” answer is 7 . How did we arrive at this? The opposite of multiplication is division. So This solution can be used as a template to solve any similar problem. The following six problems illustrate the method. 1. What is 16% of $140 ? (A missing part problem.) Solution : 2. 27 is 54% of what value? (A missing total amount.) Solution : 3. What percent of $160 is $200? (A missing percent.) Solution : 4. Solution : 5. 125% of what value is $423 ? (A missing total amount.) Solution : 6. 19 is to 80 like what number is to 300? Solution : This problem is not strictly a percent problem. However, its solution is very similar in setup to a percent problem. Here the phrase 19