# Solving Percent Problems

Identifying Amounts, Percents, and Bases

In early mathematics, students come to understand percents as an amount of the base sum of an item, but the term "per cent" simply means "per hundred," so it can be interpreted as a portion out of 100, including fractions and sometimes numbers higher than 100.

In percent problems in mathematics assignments and examples, students are often asked to identify the three core parts of the problem—the amount, the percent, and the base—wherein the amount is the number taken out of the base by being reduced by a certain percentage.

The percent symbol is read "twenty-five percent" and simply means 25 out of 100. It is useful to be able to understand that a percent can be converted to a fraction and a decimal, meaning that 25 percent can also mean 25 over 100 which can be reduced to 1 over 4 and 0.25 when written as a decimal.

## Practical Uses of Percentage Problems

Percentages may be the most useful tool of early mathematics education for adult life, especially when you consider that every mall has "15 percent off" and "half off" sales to entice shoppers to purchase their wares. As a result, it's critical for young students to grasp the concepts of calculating the amount reduced if they take a percentage away from of a base.

Imagine you're planning a trip to Hawaii with you and a loved one, and have a coupon that's only valid for the off-season of travel but guarantees 50 percent off the ticket price. On the other hand, you and your loved one can travel during the busy season and really experience the island life, but you can only find 30 percent discounts on those tickets.

If the off-season tickets cost \$1295 and the on-season tickets cost \$695 before applying the coupons, which would be the better deal? Based on the on-season tickets being reduced by 30 percent (208), the final total cost would be 487 (rounded up) while the cost for the off-season, being reduced by 50 percent (647), would cost 648 (rounded up).

In this case, the marketing team probably expected people would jump at the half-off deal and not research deals for a time when people want to travel out to Hawaii the most. As a result, some people wind up paying more for a worse time to fly!

## Other Everyday Percent Problems

Percents occur almost as frequently as simple addition and subtraction in everyday life, from calculating the appropriate tip to leave at a restaurant to calculating gains and losses in recent months.

People who work on commission often get around 10 to 15 percent of the value of the sale they made for a company, so a car's salesman who sells a one hundred thousand dollar car would get between ten and fifteen thousand dollars in commission from his sale.

Similarly, those who save a portion of their salary for paying insurance and government taxes, or wish to dedicate part of their earnings to a savings account, must determine which percentage of their gross income they want to divest to these different investments.

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