Course: 4.5 用百分比解决标记和标记问题-interactive

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以百分比解决标记和标记问题

Retro Video Games
::Retro 视频游戏游戏

A retro Nintendo 64 console with controller, illustrating vintage gaming equipment.

In business, an understanding of markups and markdowns is vital to achieving success. In this chapter, you will be assuming the role of a store owner who buys and resells retro video games and video game consoles. Here, you will be exploring some of the ways that you as a business owner c ould use your math skills to increase your profit and sales.
::在商业领域,了解加价和记分对于成功至关重要。在本章中,你将扮演一个商店老板的角色,他购买和转售回转电子游戏和视频游戏控制台。在这里,你将探索你作为企业主可以使用数学技能增加利润和销售的一些方法。

Discussion Questions
::讨论问题讨论问题

What are some ways that can increase the profit you make on an item?
::怎样才能增加你在某项目上赚到的利润呢?

What are some ways that you could bring in more customers to increase sales?
::还有什么方法可以吸引更多的顾客来增加销售?

Markups
::标记标记标记

Many businesses buy their merchandise from wholesalers and resell. Since you don’t make the video games you sell, you need to buy them. To make a profit, you must sell the video games at a higher price than the original price at which you purchased them. The amount which you increase the price to cover the cost is known as markup . For example, if you buy a video game for $20, you must sell it at more than $20 to make a profit.
::许多企业从批发商那里购买自己的商品并转售。由于你无法制造你出售的视频游戏,你需要购买这些游戏。为了盈利,你必须以高于你购买这些游戏的原价的价格出售这些电子游戏。你为支付成本而提高的价钱被称为加价。例如,如果你购买20美元的视频游戏,你必须卖20多美元才能获利。

The amount you increase the price by can be expressed as a percent of the purchase price. I ncreasing the price of an item by 25% is the same as selling it at 100% + 25% = 125% the price at which you purchased it. You can write this using decimals by saying that a markup of 25% is the same as 0.25 + 1 where 1 represents 100% of the purchase price and 0.25 is the 25% markup. In this example, the 25% which the price was increased is known as a markup rate . The selling price would be determined using the equation $\begin{aligned} part = percent \cdot whole . \end{aligned}$
::提高价格的金额可以以购买价的百分之一表示。将物品价格提高25%, 与以100%+25% = 25% = 购买价的125% = 125 = 购买价的销售额相同。您可以使用小数来写。您可以使用小数表示, 25% + 1 等于 0. 25 + 1, 其中 1 代表购买价的100%, 0. 25 等于 25% 的加价。例如, 涨价的25% 被称为加价。销售价格将使用方程式 = 百分数来确定。

Part: selling price
::部分:销售价格

Percent: 1 + markup rate
::百分比:1+加加价率

Whole: purchase price
::整个:购货价格

Discussion Question
::讨论问题

What does the 1 in the percent represent?
::百分比中的1%代表什么?

Substituting these values into the percent equation gives you the following formula for markups:
::将这些值替换为百分比方程式, 会给你以下的加分公式 :

\begin{aligned} selling price = (1 + markup rate) \cdot purchase price \end{aligned}

::售价 =(1+加加价) 购货价格

Example
::示例示例示例示例

You purchase a Nintendo 64 for $45 and plan to resell it for $63. What would the markup rate on this console be?
::你买任天堂64,45美元,计划转售63美元。这个控制台的加价是多少?

Use the formula above:
::使用上面的公式 :

$\begin{aligned} selling price = (1 + markup rate) \cdot purchase price \end{aligned}$
::售价 =(1+加加价) 购货价格

Selling Price: $63
::售价:63美元

Markup Rate: x
::标记率: x

Purchase Price: $45
::购买价格:45美元

$\begin{aligned} 63 & = (1 + x) \cdot 45 \\ \frac{63}{45} & = 1 + x \\ 1.4 & = 1 + x \\ 0.4 & = x \end{aligned}$
::63=(1+x)\\\\456345=1+x1.4=1+x0.4=x

The markup rate is 0.4. However, this formula gives us the percent as a decimal. You must convert 0.4 to a percent.
::标记率是0.4。然而, 这个公式让我们以小数点表示百分比。您必须将0. 4%转换为 0. 4% 。

Answer: The markup rate is 40%.
::答复:加价率为40%。

Use the interactive below to e xplore how markup affect the sales price of a product.
::利用下面的交互方式,探讨标记如何影响产品的销售价格。

INTERACTIVE

Markups

Use the sliders to change the Selling Price and the Markup Rate.
::使用滑块来改变售价率和标注率。

See how these affect the Purchase Price.
::看看它们如何影响购买价格。

ercent-of-increase" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f4577e52ee4709e18896fd1&collectionHandle=arithmetic&collectionCreatorID=3&conceptCollectionHandle=arithmetic-:

ercent-of-increase&mode=lite" test-id="5f4577e52ee4709e18896fd1">

Markdown s
::标记标记

A strategy that many businesses use to increase sales is to offer markdowns. A markdown can occur to bring in business, because a product can no longer be sold at its current price, etc. A markdown is an amount by which you decrease the selling price. The amount that you decrease the price by can be expressed as a percent of the selling price, known as the markdown rate.
::许多企业用来增加销售额的战略是提供记分。记分可以带来商业,因为产品不再能以现价出售,等等。记分是您降低销售价格的一个数额。你降低价格的金额可以以销售价格的百分之一表示,即记分率。

The selling price would be determined using the equation: $\begin{aligned} part = percent \cdot whole . \end{aligned}$
::销售价格将根据等式确定:部分=整个百分比。

Percent: 1 - markdown rate
::百分比: 1 - 减速率

Whole: original price
::整个:原价

Part: selling price
::部分:销售价格

Substituting these values into the percent formula gives you the following formula for markdowns:
::将这些值替换为百分数公式, 会给你以下的标记公式 :

\begin{aligned} selling price = (1 - markdown rate) \cdot original price \end{aligned}

::售价 = (1 - 马克下调率) = 原价

Example
::示例示例示例示例

You are selling a video game that you initially bought for $30. You decide to reduce the selling price to $21 in hopes to increase the likelihood of having someone buy it from you. What is the markdown rate on the game?
::您正在出售一种你最初以30美元购买的电玩游戏。您决定把售价降低到21美元, 希望增加有人从您那里购买它的可能性。游戏的减价率是多少?

Selling Price: $21
::售价:21美元

Markdown Rate: $\begin{aligned} x \end{aligned}$
::标记下降速率: x

Original Price: $30
::原价:30美元

$\begin{aligned} 21 & = (1 - x) \cdot 30 \\ \frac{21}{30} & = 1 - x \\ 0.7 & = 1 - x \\ - 0.3 & = - x \\ 0.3 & = x \end{aligned}$
::21=(1-x) 302130=1-x0.7=1-x-0.3_x0.3=x

The markdown rate is 0.3. However, this formula gives us the percent as a decimal. What is the markdown rate written as a percentage ?
::标记降幅率是0.3。但是, 这个公式让我们以小数点表示百分比。以百分比表示的标记降幅率是多少?

Use the interactive below to explore how markdown rates affect the sales price of a product.
::利用下面的交互方式,探讨减价率如何影响产品的销售价格。

INTERACTIVE

Markdowns

Use the sliders to change the Selling Price and the Markdown Rate.
::使用滑块来改变售价和标记率。

See how these affect the Original Price.
::看看这些如何影响原始价格。

ercent-of-decrease" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f4577eb0318e556783cafd1&collectionHandle=arithmetic&collectionCreatorID=3&conceptCollectionHandle=arithmetic-:

ercent-of-decrease&mode=lite" test-id="5f4577eb0318e556783cafd1">

Consecutive Markdowns
::连续标记

Stores will often offer consecutive discounts from multiple promotions.
::仓库往往提供多次晋升的连续折扣。

Example
::示例示例示例示例

A thrift store was selling an Atari 2600 for $80 before deciding to have a 40% off promotion. A customer comes in to buy the console and pays with a 10% off any one item coupon. The coupon states that the 10% off coupon applies after any in-store promotions. The customer expects to get 50% off overall and pay $4 0 .00. Is the customer correct?
::一家克里夫特商店以80美元的价格出售Atari 2600美元,然后决定加薪40%。一个顾客进来购买控制台,从任何一件优惠券中支付10%。优惠券规定,10%的优惠券适用于任何室内促销。客户预计总减薪50%,并支付40.00美元。客户是否正确?

The customer may expect to get 50% off the original price. However, this is not the case. Consecutive markdowns occur one after the other rather than at the same time. To find the price that the customer will pay we must use the markdown formula twice.
::客户可能会期望从原来的价格中扣除50%。但是,情况并非如此。连续的记分会发生一个接一个而不是同时发生。为了找到客户将支付的价格,我们必须使用两次记分公式。

$\begin{aligned} selling price = (1 - markdown rate) \cdot original price \end{aligned}$
::售价 = (1 - 马克下调率) = 原价

Selling Price: x
::售价:x

Markdown Rate: 40% or 0.4 as a decimal
::下标速率:40%或小数点为0.4

Original Price: 80
::原价:80

$\begin{aligned} x & = (1 - 0.4) \cdot 80 \\ x & = 80 (0.6) \\ x & = 48 \end{aligned}$
::x=( 1-04)_80x=80( 0. 6)x=48

Now apply the 10% off coupon.
::现在使用10%的优惠券

$\begin{aligned} selling price = (1 - markdown rate) \cdot original price \end{aligned}$
::售价 = (1 - 马克下调率) = 原价

Selling Price: x
::售价:x

Markdown Rate: 10% or 0.1 as a decimal
::下标速率:10%或小数点为0.1

Original Price: 48
::原价:48

$\begin{aligned} x & = (1 - 0.1) \cdot 48 \\ x & = 48 (0.9) \\ x & = 43.20 \end{aligned}$
::x=( 1-01)-48x=48( 0. 9)x=43.20

Discussion Question
::讨论问题

How did applying the discount after the promotion benefit the business?
::在促销后如何适用折扣使企业受益?

When taking a percent of a percent, you can rewrite the formula as follows:
::当取取百分之一的百分之一时,您可以将公式改写如下:

\begin{aligned} selling price = (1 - {markdown rate}_{1}) \cdot (1 - {markdown rate}_{2}) \cdot original price \end{aligned}

::售价 = (1 - 标记降价 ) = = (1 - 标记降价 ) = = (1 - 标记降价 ) = 原价

Use the interactive below to explore how consecutive markdown rates affect the sales price of a product.
::利用下面的交互方式,探讨连续的减价率如何影响产品的销售价格。

INTERACTIVE

Consecutive Markdowns

Use the sliders to change the Selling Price and the Markdown Rates.
::使用滑块来改变售价和标记率。

See how these affect the Original Price.
::看看这些如何影响原始价格。

ercent-problems" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f4577f756eb0f2e2d43b01a&collectionHandle=algebra&collectionCreatorID=3&conceptCollectionHandle=algebra-:

ercent-problems&mode=lite" test-id="5f4577f756eb0f2e2d43b01a">

Summary

Use the formula: $\begin{aligned} selling price = (1 + markup rate) \times purchase price \end{aligned}$ to solve problems involving markups.
::使用公式: 销售价格=(1+标记率) x 购买价格来解决涉及加价的问题。

Use the formula: $\begin{aligned} selling price = (1 + markdown rate) \times original price \end{aligned}$ to solve problems involving markups.
::使用公式: 销售价格=(1+标记下调率) x 原始价格来解决加价问题。

Section outline

General

以百分比解决标记和标记问题

Retro Video Games ::Retro 视频游戏游戏

Markups ::标记标记标记

Markdown s ::标记标记

Consecutive Markdowns ::连续标记

Retro Video Games
::Retro 视频游戏游戏

Markups
::标记标记标记

Markdown s
::标记标记

Consecutive Markdowns
::连续标记