In order to solve word problems involving percents, you should be able to:
Solving word problems involving percents is a matter
of taking the information from the problem and deciding where it belongs in the percent
The percent formula is as follows:
written as a decimal value) x (the base
) = the amount
, as indicated in the formula, is always expressed as a decimal value rather than in percent
form. The base
is sometimes considered the original value. It is the number that you are taking a percentage of. The amount
is sometimes thought of as the final answer. Let's lok at a few preliminary examples to make sure you understand how the percent
formula works before moving on to the word problems.
- What number is 12% of 80?
The percent, written as a decimal is 0.12. The base
is 80 and the amount is what we are looking for. So we have
(0.12)(80) = 9.6.
- 4.515 is 4.3% of what number?
The percent, written as a decimal is 0.043. The base
is not known and the amount is 4.515. So we have
- What percent of 400 is 3.2?
is what we are looking for. The base
is 400 and the amount is 3.2. So we have
Recall that in the percent
formula, percents are written as decimals. So the decimal form is 0.008 which means in percent
form we have 0.8%.
These three examples have shown you how to solve for each piece of the percent
formula. We now need to apply this information to solving word problems. Remember, the main task is to identify each piece of the percent
formula and then solve as we did above. Now let's use this process to work a word problem.
Suppose a retailer buys a coat for $80 and then sells it for $120. What is the percent
of markup on the coat?
The problem is telling us that we want to know the percent
value, so we need to identify the base
and the amount
to solve the problem. The value of $80 is our base. We have to be careful here because $120 is not the amount. When we take a percentage of $80, we then add that to the cost of the coat to get the selling price. In other words, the coat has been marked up $40. That is the amount we should be using. So we have the formula
Remember that when we solve the percent
formula for a percent, it gives us a decimal value that we have to change into a percent. In this case, the coat has been marked up 50%.