| Chapter 6 Percents 6-4 Solving Word Problems With Percents 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
| | 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 solt 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. Exercises Click the ? symbol to see the correct answer. | 1. | I will save ? cents when I buy an 80-cent can of peas at a 10% discount. | | 2. | A certain pair of slacks is on sale at 20% off the regular price. If the regular price is $48, you will save ? | | 3. | A piece of jewlery that is normally priced at $780 is marked at 50% off the regular price. You can save ? by taking advantage of the sale. | | 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 = Regualr 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 | Percents and Sales Taxes 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 | | Thinking Mathematically 
This graphic shows: - Total price = Purchase price + Sales tax
- Purchase price = Total price – Sales tax
- Sales tax = Total price – Purchase price
| | Percents and Commissions | Thinking Mathematically 
This graphic shows: - Total pay = Salary + Commission
- Salary = Total pay – Commission
- Commission = Total pay – Salary
| | Percents and Simple Interest Percent Increase and Percent Decrease Here are some typical percent-increase problems: - The number of people shopping at local toy stores 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 decreased 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 increase: Percent increase = | Amount of increase | x 100 | Original amount | | Here are some typical percent-decrease problems: Procedure To find the percent of decrease: Percent decrease = | Amount of decrease | x 100 | Original amount | | Example A box contains 23 blue marbles and 41 red marbles. What percentage of the marbles are 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% | |
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