Section: 查找贴现价格 | 5.14 寻找贴现价格

Section outline

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?
::Jeremiah在当地一家书店工作,说服他的老板从所有销售中扣除30%。销售税是5%。一本封面价格为15.99美元的书的总价格是多少?

In this concept, you will learn to find discount prices given sales.
::在此概念中,您将学会找到贴现价格给销售。

Sale Prices
::销售价格

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.
::为了减少库存或激励买家,商店常常有销售量,销售价格贴现率为1%。与其提高百分比,不如降低百分比,从而导致销售价格下降。

Let’s look at an example.
::让我们举个例子。

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?
::夏季结束时,一家服装店出售所有游泳服,折扣60%。如果比基尼的正常价格为29.99美元,销售价格是多少?

First, multiply the original price by the percent decrease. Remember that percent means the denominator is 100.
::首先,将原价乘以下降百分比。记住百分比意味着分母为100。

$\begin{aligned} \begin{array}{rcl} 29.99 \times \frac{60}{100} & = & \frac{1799.4}{100} \\ = & 17.994 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 29.99 \times \frac{60}{100} &=& \frac{1799.4}{100} \\ &=& 17.994 \end{array}\end{align*}$ Next, subtract the amount of decrease from the original price.

$\begin{aligned} 29.99 - 17.994 = 11.996 \end{aligned}$
$\begin{align*}29.99 - 17.994 = 11.996 \end{align*}$

The answer is 11.996.
::答案是11.996。

The sale price of the bikini is $12.00.
::比基尼的销售价是12美元

If the sales tax is 6.25%, what is the final price of the discounted bikini?
::如果销售税是6.25%,折扣比基尼的最后价格是多少?

First, multiply the sale price by the sales tax. Remember that percent means the denominator is 100.
::首先,将销售价格乘以销售税。记住百分比意味着分母为100。

$\begin{aligned} \begin{array}{rcl} 12.00 \times \frac{6.25}{100} & = & \frac{75}{100} \\ = & 0.75 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 12.00 \times \frac{6.25}{100} &=& \frac{75}{100} \\ &=& 0.75 \end{array}\end{align*}$

Next, add the sales tax to the sale price.
::接下来,在销售价格中加上销售税。

$\begin{aligned} 12.00 + 0.75 = 12.75 \end{aligned}$
$\begin{align*}12.00 + 0.75 = 12.75\end{align*}$

The answer is 12.75.
::答案是12.75。

The total price of the bikini is $12.75.
::比基尼的总价格是12.75美元。

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?
::以税收计算价格与增长百分比相同。如果你知道包括税收在内的总价格,并想知道产品的原始价格呢?

Let’s look at an example.
::让我们举个例子。

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?
::商店办事员对DVD播放机收取78.75美元。您的地区税率是5%。DVD播放机的原价是多少?

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:
::首先,为了获得总成本,现金登记册计算5%的税,并将税额加到原价上。换句话说:

$\begin{aligned} Original Price + 5 % of Original Price = Total Cost \end{aligned}$
$\begin{align*}\text{Original Price} + 5 \% \ \text{of Original Price} = \text{Total Cost}\end{align*}$
::原始价格+原价格=总成本的5%

Let $\begin{align*}p\end{align*}$ represent the original price and $\begin{align*}c\end{align*}$ represent the total cost, the equation becomes:
::p代表原价,c代表总成本,等式如下:

$\begin{aligned} p + 0.05 p = c or 1.05 p = c \end{aligned}$
$\begin{align*}p + 0.05 \ p= c \qquad \ \text{or}\qquad \ 1.05 \ p = c\end{align*}$
::p+0.05p=c或1.05p=c

In this case, if you are given $\begin{align*}p\end{align*}$ , you can solve for $\begin{align*}c\end{align*}$ . Or if you are given $\begin{align*}c\end{align*}$ , you can solve for $\begin{align*}p\end{align*}$ .
::在这种情况下,如果给p,您可以解决 c.,或者如果给c,您可以解决p.。

Next, fill in what you know. In this example, you paid a total cost, $\begin{align*}c\end{align*}$ , of $78.75. Substitute $\begin{align*}c\end{align*}$ in the equation.
::接下来,填上你所知道的。在这个例子中,你付出了78.75美元的总成本。

$\begin{aligned} \begin{array}{rcl} 1.05 p & = & c \\ 1.05 p & = & 78.75 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 1.05 \ p &=& c \\ 1.05 \ p &=& 78.75 \end{array}\end{align*}$
::1.05p=c1.05p=78.75

Then, divide both sides by 1.05 to solve for $\begin{align*}p\end{align*}$ .
::然后把两边除以1.05 解决p

$\begin{aligned} \begin{array}{rcl} 1.05 p & = & 78.75 \\ \frac{1.05 p}{1.05} & = & \frac{78.75}{1.05} \\ p & = & 75 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 1.05 \ p &=& 78.75 \\ \frac{1.05 \ p}{1.05} &=& \frac{78.75 }{1.05} \\ p &=& 75 \end{array}\end{align*}$
::1.05p=78.751.05p1.05=78.751.05p=75

The answer is 75.
::答案是75

The original price was $75.00
::原价75.00美元

Let’s try another one.
::让我们再试一次。

You are charged $29.10 for an item with 7% tax included. What was the original price of the item?
::包括7%的税费。物品的原价是多少?

First, write an equation.
::首先,写一个方程。

$\begin{aligned} p + 0.07 p = c or 1.07 p = c \end{aligned}$
$\begin{align*}p + 0.07 \ p = c \qquad \text{or} \qquad 1.07 \ p = c\end{align*}$
::p+0.07p=cor1.07p=c

Next, fill in what you know. In this example, you paid a total cost, $\begin{align*}c\end{align*}$ , of $29.10. Substitute $\begin{align*}c\end{align*}$ in the equation.
::接下来,填上你所知道的。在这个例子中,你支付了29.10美元的总成本,C。在方程中,替代C。

$\begin{aligned} \begin{array}{rcl} 1.07 p & = & c \\ 1.07 p & = & 29.10 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 1.07 \ p &=& c \\ 1.07 \ p &=& 29.10 \end{array}\end{align*}$
::1.07p=c1.07p=29.10

Then, divide both sides by 1.07 to solve for $\begin{align*}p\end{align*}$ .
::然后把两边除以1.07 解决p

$\begin{aligned} \begin{array}{rcl} 1.07 p & = & 29.10 \\ \frac{1.07 p}{1.07} & = & \frac{29.10}{1.07} \\ p & = & 27.196 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 1.07 \ p &=& 29.10 \\ \frac{1.07 \ p}{1.07} &=& \frac{29.10 }{1.07} \\ p &=& 27.196 \end{array}\end{align*}$ The answer is 27.196.
::1.07 p=29.101.07 p1.07=29.101.07p=27. 196 答案是27.196。

The original price was $27.20.
::原价27.20美元。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Jeremiah’s bookstore sale.
::更早之前, 你曾得知Jeremiah的书店销售问题,

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.
::你买了一本书15.99美元,然后在购买书时必须缴纳5%的销售税。

First, calculate the discount on the purchase.
::首先,计算购买的折扣。

$\begin{aligned} \begin{array}{rcl} 15.99 \times \frac{30}{100} & = & \frac{479.7}{100} \\ = & 4.797 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 15.99 \times \frac{30}{100} &=& \frac{479.7}{100} \\ &=& 4.797 \end{array}\end{align*}$

Next subtract the discount from the original price to find the price of your book.
::下一步从原始价格中减去折扣,以找到您的书籍的价格。

$\begin{aligned} 15.99 - 4.797 = 11.193 \end{aligned}$
$\begin{align*}15.99 - 4.797 = 11.193\end{align*}$

Then, calculate the sales tax. The price of the book, $\begin{align*}p\end{align*}$ , is $11.19. You are looking for the cost, $\begin{align*}c\end{align*}$ .
::然后计算销售税。这本书的价格,p,是11.19美元。你正在寻找成本,c。

$\begin{aligned} \begin{array}{rcl} c & = & 1.05 p \\ c & = & 1.05 (11.19) \\ c & = & 11.7495 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} c &=& 1.05 \ p \\ c &=& 1.05 (11.19) \\ c &=& 11.7495 \\ \end{array}\end{align*}$
::c=11.7495=11.7495=1.05pc=1.05(11.19)c=11.7495

The answer is 11.7495.
::答案是11.7495

The final price is $11.75.
::最后价格为11.75美元。

Example 2
::例2

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?
::布伦达为她的花园购买一些植物。两棵树每棵价格为55美元。六张郁金香每张价格为2.50美元。布伦达购买税为5.75 % , 但对于十点前露面的人(布伦达也这样做了 ) , 整个购买的早鸟特价为10 % 。布伦达的总成本是多少?

First, add up all of your purchases before tax and discounts.
::首先,加起来你所有的购买之前税和折扣。

$\begin{aligned} 2 trees + 6 tulips \end{aligned}$
$\begin{align*}2 \ \text{trees} + 6 \ \text {tulips} \\\end{align*}$

$\begin{aligned} 2 \times 55 + 6 \times 2.50 = 125 \end{aligned}$
$\begin{align*}2\times 55 + 6 \times 2.50 = 125\end{align*}$

Next, calculate the total cost after sales tax.
::接下来,计算销售税之后的总成本。

$\begin{aligned} \begin{array}{rcl} c & = & 1.0575 p \\ c & = & 1.0575 \times 125 \\ c & = & 132.1875 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} c &=& 1.0575 \ p \\ c &=& 1.0575 \times 125 \\ c &=& 132.1875 \\ \end{array}\end{align*}$
::c= 1.0575pc=1.0575×125c=132.1875

Next, calculate the discount on the purchase.
::接下来,计算购买的折扣。

$\begin{aligned} \begin{array}{rcl} 132.1875 \times \frac{10}{100} & = & \frac{1321.875}{100} \\ = & 13.21875 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 132.1875 \times \frac{10}{100} &=& \frac{1321.875} {100} \\ &=&13.21875 \end{array}\end{align*}$ Then, subtract the discount from the total price to find the price paid.

$\begin{aligned} 132.1875 - 13.21875 = 118.96875 \end{aligned}$
$\begin{align*}132.1875 - 13.21875 = 118.96875\end{align*}$

The answer is 118.96875.
::答案是118.968775。

The final price Brenda paid for the trees and tulips is $118.97.
::布伦达为树木和郁金香支付的最后价钱是118.97美元。

Example 3
::例3

The original price is $27.50. Find the new price given a discount of 30%.
::原始价格为27.50美元,找到新的价格,折扣30%。

First, calculate the discount on the purchase.
::首先,计算购买的折扣。

$\begin{aligned} \begin{array}{rcl} 27.50 \times \frac{30}{100} & = & \frac{825}{100} \\ = & 8.25 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 27.50 \times \frac{30}{100} &=& \frac{825}{100} \\ &=& 8.25 \end{array}\end{align*}$

Next, subtract the discount from the original price to find the price paid.
::其次,从原价中减去折扣,以找到已支付的价格。

$\begin{aligned} 27.50 - 8.25 = 19.25 \end{aligned}$
$\begin{align*}27.50 - 8.25 = 19.25\end{align*}$

The answer is 19.25.
::答案是19.25。

The final price is $19.25.
::最后价格为19.25美元。

Example 4
::例4

The original price is $545.00. Find the new price given a discount of 30%.
::原价是545.00美元。找到新价, 给予30%的折扣。

First, calculate the discount on the purchase.
::首先,计算购买的折扣。

$\begin{aligned} \begin{array}{rcl} 545.00 \times \frac{30}{100} & = & \frac{16350}{100} \\ = & 163.5 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 545.00 \times \frac{30}{100} &=& \frac{16350}{100} \\ &=& 163.5 \end{array}\end{align*}$

Next, subtract the discount from the original price to find the price paid.
::其次,从原价中减去折扣,以找到已支付的价格。

$\begin{aligned} 545.00 - 163.50 = 381.50 \end{aligned}$
$\begin{align*}545.00 -163.50 = 381.50\end{align*}$

The answer is 381.50.
::答案是381.50

The final price is $381.50.
::最后价格为381.50美元。

Example 5
::例5

The original price is $75.80. Find the new price given a discount of 30%.
::原始价格是75.80美元。找到新的价格, 给予30%的折扣。

First, calculate the discount on the purchase.
::首先,计算购买的折扣。

$\begin{aligned} \begin{array}{rcl} 75.80 \times \frac{30}{100} & = & \frac{2274}{100} \\ = & 22.74 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 75.80 \times \frac{30}{100} &=& \frac{2274}{100} \\ &=& 22.74 \end{array}\end{align*}$

Next, subtract the discount from the original price to find the price paid.
::其次,从原价中减去折扣,以找到已支付的价格。

$\begin{aligned} 75.80 - 22.74 = 53.06 \end{aligned}$
$\begin{align*}75.80 - 22.74 = 53.06\end{align*}$

The answer is 53.06.
::答案是53.06

The final price is $53.06.
::最后价格是53.06美元。

Review
::回顾

Your food bill at a restaurant is $85.77. Calculate the total cost given the following possible tips. Round to the nearest whole cent.
::您在餐馆的食品费用是85.77美元。计算总成本时,可以给出以下提示。整数到最近的整数。

1. Service 10%
::1. 服务10%

2. Decent service 15%
::2. 体面服务 15%

3. Great service 20%
::3. 大服务 20%

4. Outstanding service 25%
::4. 未缴摊款 25%

5. Poor service 5%
::5. 服务差5%

What was the original price given total cost and tax rate? Be sure to round when necessary.
::总成本和税率的最初价格是多少? 必要时一定要四舍五入。

6. Total cost: $1475.68 tax rate: 7%
::6. 总费用:1475.68美元税率:7%

7. Total cost: $63.80 tax rate: 4.5%
::7. 总费用:63.80美元税率:4.5%

8. Total cost: $55.90 tax rate: 4%
::8. 总费用:55.90美元税率:4%

9. Total cost: $80.20 tax rate: 2.5%
::9. 总费用:80.20美元税率:2.5%

10. Total cost: $120.00 tax rate: 5%
::10. 费用总额:120美元税率:5%

11. Total cost: $99.50 tax rate: 2%
::11. 总费用:99.50美元的税率:2%

12. Total cost: $155.30 tax rate: 3%
::12. 总费用:155.30美元税率:3%

13. Total cost: $250.75 tax rate: 3.5%
::13. 总费用:250.75美元税率:3.5%

Solve each problem. There are several steps to solving each problem. Be sure to round when necessary.
::解决每个问题。解决每个问题有几个步骤。必要时务必进行回合。

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 on top of this. How much do you owe for the taxi ride if the meter shows $45?
::14. 你在一个外国搭乘出租车,在那里,他们为深夜旅行增加20%的总数。司机预计还会增加15%的提示。如果计时表显示45美元,你欠出租车多少钱?

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?
::15. 母亲节时,你带母亲去吃龙虾,龙虾盘子每盘24.95美元,但包括饮料和甜点自助餐,服务员也是母亲,所以你给她留了20%的小费,不过,你带了25 %的优惠券,2个人的总费用是多少?

Review (Answers)
::回顾(答复)

Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键。

Resources
::资源

Section outline

Sale Prices ::销售价格

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Sale Prices
::销售价格

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源