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# Prices Involving Discounts

## Determine the value of a number that has been reduced by a given percentage.

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Practice Prices Involving Discounts
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Find Discount Prices Given Sales

Credit: Sahron and Nikki McCutcheon

Jeremiah works at a local bookstore and convinced his boss to have a 30% off everything sale. The sales tax is 5%. What is the total price on a book whose cover price is $15.99? In this concept, you will learn to find discount prices given sales. ### Guidance In order to reduce inventories or motivate buyers, stores often have sales in which they discount prices by a percent. Instead of a percent increase, this is a percent decrease, which results in a sale price. Let’s look at an example. At the end of the summer, a clothing store puts all swimwear on sale. They offer a discount of 60%. If the regular price is$29.99 on a bikini, what is the sale price?

First, multiply the original price by the percent decrease. Remember that percent means the denominator is 100.

29.99×60100==1799.410017.994
Next, subtract the amount of decrease from the original price.

29.9917.994=11.996

The sale price of the bikini is $12.00. If the sales tax is 6.25%, what is the final price of the discounted bikini? First, multiply the sale price by the sales tax. Remember that percent means the denominator is 100. 12.00×6.25100==751000.75 Next, add the sales tax to the sale price. 12.00+0.75=12.75 The answer is 12.75. The total price of the bikini is$12.75.

Calculating a price with tax is the same as increasing by a percent. What if you know the total price including the tax and want to know the original price of a product?

Let’s look at an example.

A store clerk charges you 78.75 for a DVD player. The tax in your area is 5%. So how much was the original price of the DVD player? First, in order to get the total cost, the cash register computes the 5% tax and adds the tax to the original price. In other words: Original Price+5% of Original Price=Total Cost Let p\begin{align*}p\end{align*} represent the original price and c\begin{align*}c\end{align*} represent the total cost, the equation becomes: p+0.05 p=c or 1.05 p=c In this case, if you are given p\begin{align*}p\end{align*}, you can solve for c\begin{align*}c\end{align*}. Or if you are given c\begin{align*}c\end{align*}, you can solve for p\begin{align*}p\end{align*}. Next, fill in what you know. In this example, you paid a total cost, c\begin{align*}c\end{align*}, of78.75. Substitute c\begin{align*}c\end{align*} in the equation.

1.05 p1.05 p==c78.75

Then, divide both sides by 1.05 to solve for p\begin{align*}p\end{align*}.

1.05 p1.05 p1.05p===78.7578.751.0575

The original price was $75.00 Let’s try another one. You are charged$29.10 for an item with 7% tax included. What was the original price of the item?

First, write an equation.

p+0.07 p=cor1.07 p=c

Next, fill in what you know. In this example, you paid a total cost, c\begin{align*}c\end{align*}, of 29.10. Substitute c\begin{align*}c\end{align*} in the equation. 1.07 p1.07 p==c29.10 Then, divide both sides by 1.07 to solve for p\begin{align*}p\end{align*}. 1.07 p1.07 p1.07p===29.1029.101.0727.196 The answer is 27.196. The original price was27.20.

### Guided Practice

Brenda purchases some plants for her gardens. Two trees have a price of $55.00 each. Six tulips cost$2.50 each. The tax on Brenda’s purchase is 5.75% but there is an early-bird special of 10% off the entire purchase to those who show up before 10 am (which Brenda did). What is Brenda’s total cost?

2 trees+6 tulips

2×55+6×2.50=125

Next, calculate the total cost after sales tax.

ccc===1.0575 p1.0575×125132.1875

Next, calculate the discount on the purchase.

132.1875×10100==1321.87510013.21875
Then, subtract the discount from the total price to find the price paid.

132.187513.21875=118.96875

The final price Brenda paid for the trees and tulips is $118.97. ### Examples #### Example 1 The original price is$27.50. Find the new price given a discount of 30%.

First, calculate the discount on the purchase.

27.50×30100==8251008.25

Next, subtract the discount from the original price to find the price paid.

27.508.25=19.25

The final price is $19.25. #### Example 2 The original price is$545.00. Find the new price given a discount of 30%.

First, calculate the discount on the purchase.

545.00×30100==16350100163.5

Next, subtract the discount from the original price to find the price paid.

545.00163.50=381.50

The final price is $381.50. #### Example 3 The original price is$75.80. Find the new price given a discount of 30%.

First, calculate the discount on the purchase.

75.80×30100==227410022.74

Next, subtract the discount from the original price to find the price paid.

75.8022.74=53.06

The final price is $53.06. ### Follow Up Credit: Hans Dinkleberg Source: https://www.flickr.com/photos/uitdragerij/3100252985/in/photolist-5HXBcF-5qvC43-cCVUH7-ebZL31-bniKn4-5SnUqc-fsKKHe-918vgB-aorQ1b-ciakYm-HLVXC-atLs3M-atLrYB-atLrTR-m6Cxw9-6UiBSN-5E2ha4-ftvYoL-6etRv8-8eBwKy-eeu9BC-85yR4q-7Uv9gU-eeoq4t-di5Vur-pirnFW-9GQx74-918v1D-61HpCQ-oqrWiu-5V5Z1X-dQHxno-61Trms-adZwGs-4Lze1E-4Jn5aW-918vB8-apeRbm-5mi8ko-hzVjak-6MqCzo-qn8gDU-8qKDut-78hXjd-4r6Kpc-8JgzWr-7CQx2c-fhrV2w-4HQ1fs-cUMW57 License: CC BY-NC 3.0 Remember Jeremiah’s bookstore sale? They have a 30% off any book sale. You bought a book for$15.99 and then had to pay 5% sales tax on the book purchase.

First, calculate the discount on the purchase.

15.99×30100==479.71004.797

Next subtract the discount from the original price to find the price of your book.

15.994.797=11.193

Then, calculate the sales tax. The price of the book, p\begin{align*}p\end{align*}, is 11.19. You are looking for the cost, c\begin{align*}c\end{align*}. ccc===1.05 p1.05(11.19)11.7495 The answer is 11.7495. The final price is11.75.

### Explore More

Your food bill at a restaurant is $85.77. Calculate your total cost after each of the following. Be sure to round when necessary. 1. Service 10% 2. Decent service 15% 3. Great service 20% 4. Outstanding service 25% 5. Poor service 5% What was the original price given total cost and tax rate? Be sure to round when necessary. 6. Total cost:$1475.68 tax rate: 7%

7. Total cost: $63.80 tax rate: 4.5% 8. Total cost:$55.90 tax rate: 4%

9. Total cost: $80.20 tax rate: 2.5% 10. Total cost:$120.00 tax rate: 5%

11. Total cost: $99.50 tax rate: 2% 12. Total cost:$155.30 tax rate: 3%

13. Total cost: $250.75 tax rate: 3.5% Solve each problem. There are several steps to solving each problem. Be sure to round when necessary. 14. You take a taxi ride in a foreign country where they add 20% to your total for late night travel. The driver expects an additional 15% tip. How much do you owe for the taxi ride if the meter shows$45?

15. You take your mother out for lobster for Mother’s Day. The lobster platters are \$24.95 each but include the drink and dessert buffet. Your waitress is a mother, too, so you leave her a 20% tip. However, you did bring a coupon for 25% off. What is your total cost for 2 people?

### Vocabulary Language: English

Markup

Markup

The markup is the difference between the wholesale price and the retail price.
Wholesale price

Wholesale price

The wholesale price is the price that a merchant pays when they purchase a product from a manufacturer.