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Chapter 7—Percents
7-4 Solving Percent Word Problems
This section is being expanded or revised. Please excuse the appearance of odd bits and pieces.
Percents and Sale Prices
People like to take advantage of special sale prices at retail stores. "One day only! 25% off everything in the store!" This is a 25% markdown; and when you are shopping for bargains this way, it's nice to be able to estimate how much you will save and what you will pay at the cash register. | Thinking Mathematically This graphic shows: - Regular price = Sale price + Amount saved
- Amount saved = Regular price – Sale price
- Sale price = Regular price – Amount saved
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Amount Saved
Procedure Use this formula to find the amount that you will save by buying an item on sale: Amount Saved = Regular Price x Percent Discount |
Examples
- A certain wristwatch normally sells for $128.95. How much is taken off the normal price when it is sold at a 10% discount?
Amount Reduced = Regular Price x Percent Discount
- Amount Reduced = $128.90 x 10%
- Amount Reduced = $12.89
In other words, this wristwatch is selling $12.89 below its normal price.
- How much will you save on the purchase of new automobile if it normally sells for $22,500, and you are waiting for the dealer to announce a 12% discount?
Amount Reduced = Regular Price x Percent Discount
- Amount Reduced = $22,500 x 12%
- Amount Reduced = $2700
In other words, you can save $2700 by waiting for the sale.
Examples & Exercises
Amount Saved with a Sale Price Use these interactive Examples & Exercises to strengthen your understanding and build your skills: | |
Sale Price
Naturally we are interested in knowing how much money we can save by purchasing sale-priced items. However, we also need to know how much we can expect to pay for an item that is on sale. We have seen how we can save $15 when we buy a $100 item at a 15% discount. But what can we expect to actually pay for the item at the cash register? Basically, we simply subtract the amount we save from the normal price. We figure, for instance, that we can save $15 when we buy a $100 item at a 15%. What is the price at the cash register? Just subtract the $15 savings from the normal $100 price tag: sale price = $100 – $15 = $85. | Sale price = Regular price – Amount saved |
Procedure To find the actual sales price of a discounted item: - Determine the amount saved.
- Subtract the amount saved from the normal (not-on-sale) price.
Sale Price = Regular Price – Amount Saved |
Examples
Examples & Exercises
Sale Price Use these interactive Examples & Exercises to strengthen your understanding and build your skills: | |
Percent Off the Sale Price
Percents and Sales Taxes
| Thinking Mathematically This graphic shows: - Total price = Purchase price + Sales tax
- Purchase price = Total price – Sales tax
- Sales tax = Total price – Purchase price
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Procedure To find the total price of a purchase that is subject to sales tax, determine the amount of sales tax and add it to the purchase price:: Total price = Purchase price + Sales tax |
Examples
Examples & Exercises
Use these interactive Examples & Exercises to strengthen your understanding and build your skills: | |
Percents and Commissions
| Thinking Mathematically This graphic shows: - Total pay = Salary + Commission
- Salary = Total pay – Commission
- Commission = Total pay – Salary
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Percents and Simple Interest
Percent Increase and Percent Decrease
Here are some typical percent-increase/decrease problems:
- The number of people shopping at local toy stores increased from 12,000 in October to 22,000 in November. What is the percent of increase?
- Over the past 20 years, the average annual temperature in our town dropped from 58º F to 56º F. What is the percent of decrease?
- Our electric bill increased from $88 per month to $94 per month. What is the percent of increase?
Procedure To find the percent of difference: Percent of change = | Amount of increase or decrease | x 100 | Original amount | |
Examples
Examples & Exercises
Percent of Change Use these interactive Examples & Exercises to strengthen your understanding and build your skills: | |
Example
A box contains 23 blue marbles and 41 red marbles. What percentage of the marbles is red?
The percentage of red marbles is found by multiplying the ratio of red marbles to the total number of marbles—NOT the ratio of red marbles to blue marbles.
Percent of red marbles = | Number of red marbles | x 100 |
Total number of marbles |
Percent of red marbles = | 41 red | x 100 |
23 blue + 41 red |
Percent of red marbles = | 41 red | x 100 |
64 marbles |
Percent of red marbles = | 41 red | x 100 |
64 marbles |
So the percent of red marbles = 64%
Example
Four students in our class have brown hair, 8 have blonde hair, 10 have black hair, and 3 have no hair. What percent has black hair?
Percent black hair = | Number with black hair | x 100 |
Total number of students |
Percent black hair = | 10 with black hair | x 100 |
4 + 8 + 10 + 3 students |
Percent black hair = | 10 with black hair | x 100 |
25 students |
Percent black hair = | 0.4 x 100 = 40% | |