Solving Percentage Problems in Algebra

6 Questions

If an item is originally priced at $120 and there's a 25% discount, what will be the final price after the discount?

$100

When a quantity increases by 150%, how many times larger does it become?

2 times

What is the decimal equivalent of 60%?

0.6

If a quantity is reduced by 40%, what percentage remains of the original quantity?

70%

When a quantity is doubled, what percentage increase does it represent?

100%

If something is priced at $80 and there's a 30% sale, what will be the sale price?

$64

Study Notes

A percentage is simply a fraction using percent symbols instead of fractions. In algebraic terms, it can be written as a% = $\frac{a}{100}$. To solve percentage problems, you need to know what kind of problem you're dealing with, such as how much money does one group have compared to another group?. There are several types of common percentage problems:

Percentages less than 100%: These are straightforward—just divide by 100 to get the answer, so if something costs $50, and there's a 70% sale, that means it will cost (70%\cdot50=35) dollars after the discount.
Percentages more than 100%: This is just like dividing by numbers bigger than 100; so for example, if you want to find out what $80 would become if its value increased by 120%, you multiply it by 1.2 to make it larger. So in this case, (80\times1.2=96).
Decimal equivalents: Look at the decimal equivalent of any number expressed as a percentage; for instance, 30% equals 0.3. And since the percent symbol isn't used multiplicatively, you can see that multiplying by 100 gives you the original number back again.

Percentages are useful because they help us compare things easily when their values change over time. They also allow you to express proportions without having to go through all the math involved in finding quotients.