1.7 – Percents
There are three types of percent problems.
|What is 30% of 250?|
|This is the first type of percent problem. We will want to begin by writing it as a mathematical equation:
Notice that we change the percentage to a decimal in order to use it in an equation. We will typically do this any time we use a percent mathematically. We can solve this equation simply enough by multiplying:
|25 is what percent of 400?|
|This is the second type of percent problem. Let’s rewrite it in a mathematical equation:
Here, we can divide each side of the equation by 400:
And then solve by performing the division:
Notice here that when we solve for , we have a decimal. The question, however, asked for a percent, so we must convert this. We have
|8 is 12.5% of what number?|
|This is the third type of percent problem, translating into a mathematical equation gives:
Discount and Markup
Discounts and Markups are an application of percents:
|A retail store sells t-shirts for $50. If they go on sale for 25% off, what is the discount, and what is the new sales price?|
|To find the discount amount, we simply need to find the value that is 25% of $50. That is, we need to solve the equation:
Solving this equation simply involves multiplying the right hand side:
So the discount is $12.50.To find the sale price then, we simply subtract the discount from the original price of the shirt.
So the sales price is $37.50
|A retail store purchases jeans at a price of $12 per pair. They then markup the price of the jeans by 40%. What is the markup, and the selling price of the jeans?|
|The markup is found by multiplying the markup percent by the purchase price:
So the markup is $4.80The selling price of the jeans then is found by adding the markup to the purchase price.
The jeans are sold for $16.80
Percent Increase and Percent Decrease
Percent increase is the measure of an increase, as a percentage of the original value.
|Percent Increase can be found by the formula
|Jill pays rent of $400. Her landlord raises her rent to $420. What was her percent increase?|
|Jill’s new rent is $420, and her old rent was $400. Plugging these values into the formula yields:
Percent Decrease is a measure of decrease, as a percent of the original amount.
|Percent decrease is calculated very similarly to percent increase. It is, however, slightly different. The formula for percent decrease is:
|Trent usually purchases $320 worth of chicken feed every month. One month, he only purchases $240 worth. What was the percent decrease in his purchase?|
|Notice that for percent decrease, only the order of the difference in the numerator has changed. – We can substitute the values into this formula and simplify: