Course: 4.9 解决涉及税务、委员会和收费的问题-interactive

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解决涉及税务、委员会和收费的问题

Sales Tax
::销售销售税

You go to a store and purchase an item listed at $9.99 but the cashier charges you more than $10. What happened? Unless you live in Delaware, Montana, New Hampshire or Oregon, this has likely happened to you. This happens because of something called sales tax .
::你去了一家商店,购买了99美元上市的物品但是出纳费超过10美元。发生了什么事?除非你住在特拉华州、蒙大拿州、新罕布什尔州或俄勒冈州,否则这很可能发生在你身上。这是因为所谓的销售税。

A state sales tax is a tax paid to a state government for specific goods and services. The items that the sales tax applies to depend on the state. State governments put the money from the sales tax toward police, firefighters, parks, and much more.
::国家销售税是对州政府特定商品和服务的税收。销售税适用的项目取决于州。州政府将销售税中的钱捐给警察、消防员、公园等等。

Use the image below to find the sales tax in your state.
::使用下方的图像查找您所在国家的销售税。

Map of the U.S. showing combined state and local sales tax rates by state as of 2019.

Zach lives in Rhode Island, where the sales tax is 7% and is planning to buy a cell phone which could cost anywhere between $100 and $1,000.
::Zach住在罗德岛,销售税为7%,并计划购买一部手机,可能花费100美元至1 000美元。

Use the interactive below to investigate how the price of the phone influences the sales tax.
::使用以下互动方式调查电话价格如何影响销售税。

INTERACTIVE

Tax

Use the slider to see the initial price of the phone.
::使用滑块查看手机的初始价格。

See how the sales tax changes the total price.
::看看销售税如何改变总价格。

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ercent-problems&mode=lite" test-id="5f45763de0078a0a4e121d48">

Example
::示例示例示例示例

Zach settles on a phone that costs $600. How much will the phone cost with a tax of 7%?
::Zach用一个耗资600美元的电话结算。 7%的税要花多少电话费?

Method 1 : Solve for the tax and add it to the original price .
::方法1:解决征税问题,将其添加到原价中。

To find the tax , you will need the percent formula : $\begin{aligned} part = percent \cdot whole \end{aligned}$
::要找到税收, 您需要百分比公式: part =% = 全部 =% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

Part: x
::部分:xx

Percent: 7% → 0.07
::百分比:7% + 0.07

Whole: 600
::整个:600

Since the taxed amount is part of the sales price, the taxed amount will be the part, and the sales price will be the whole.
::由于征税额是销售价格的一部分,因此征税额将是销售价格的一部分,销售价格将是整个销售价格。

$\begin{aligned} part & = percent \cdot whole \\ x & = 0.07 \cdot 600 \\ x & = 42 \end{aligned}$
::部分=百分数=0.07-600x=42

The tax is $42. To find the total amount that you will have to pay, add the tax to the sales price.
::税额为 42 美元。要找到您必须支付的总额, 请在销售价格中加上税额。

Answer: The phone will cost $600 + $42 = $642 with tax.
::答:电话费600美元+42美元=642美元加税。

Method 2 : Solve for the total.
::方法2:解决总额问题。

This method will take you straight to the answer. You will still use the equation $\begin{aligned} part = percent \cdot whole, \end{aligned}$ but this time, the part will be the total paid and the whole will be the original price. The percent will reflect the total paid relative to the original price.
::此方法会直接将您带到答案。您仍然会使用方程式部分=% 整体, 但这一次, 部分将是总支付额, 整体将是原始价格。百分比将反映相对于原始价格的总支付额。

Part: x
::部分:xx

Percent: 100% + 7% = 107% → 1.07
::百分比:100% + 7% = 107% + 1.07

Whole: 600
::整个:600

$\begin{aligned} part & = percent \cdot whole \\ x & = 1.07 \cdot 600 \\ x & = 642 \end{aligned}$
::部分=百分数=1.07-600x=642

Answer: The phone will cost a total of $642 including sales tax.
::答复:电话费用共计642美元,包括销售税。

INTERACTIVE

Identifying State Tax

Given the sales information in the interactive, which state are you in?
::根据互动中的销售信息, 你处于哪个状态?

Enter the postal code into the box for a possible state you are in after calculating tax, based on the map above.
::根据上述地图计算税后,您可能处于何种状态,请在框中输入邮政编码。

Press the white button after finding the correct answer to try another problem.
::在找到正确答案以尝试另一个问题后按下白色按钮。

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ercent-problems&mode=lite" test-id="5f45764316673a8d1a513e20">

Commission
::贸委员会委员会委员会,委员会

Commissions are commonly used in sales. A commission is a percent of a sale that a salesperson receives in addition to their pay. Companies use commission as a strategy to encourage employees to sell more. The more that an employee sells, the more money they employee make. C ommissions are common in fields like real estate , car sales, furniture sales, insurance, and many more.
::佣金通常用于销售。佣金是销售人员除工资外收到的销售额的百分之一。公司使用佣金作为鼓励雇员更多销售的战略。雇员卖得越多,他们赚得的钱就越多。佣金在房地产、汽车销售、家具销售、保险等领域很常见。

In this next example, u se the "Part, Percent, Whole" formula to calculate commissions.
::在下一个例子中,使用“部分、百分比、整体”公式计算佣金。

Example
::示例示例示例示例

Paul is a realtor that receives a 3% commission on the final sale of a house. If he sells the house for $370,000, what will his commission be?
::Paul是一个房地产商,在最终出售房屋时获得3%的佣金。如果他以370,000美元卖掉房子,他的佣金会是什么?

To solve this problem, you will again use the f ormula $\begin{aligned} part = percent \cdot whole . \end{aligned}$ Since the amount of the commission is calculated as a fraction of the selling price of the house, the commission will be the part and the price of the house will be the whole.
::为了解决这个问题, 您将再次使用公式部分 = 百分数。由于佣金金额是按房屋售价的一小部分计算, 佣金将是部分, 而房屋的价格将是全部。

Part: x
::部分:xx

Percent: 3% = 0.03
::百分比:3% = 0.03

Whole: 370,000
::整个:370,000

$\begin{aligned} part & = percent \cdot whole \\ x & = 0.03 \cdot 370, 000 \\ x & = 11, 100 \end{aligned}$
::部分=百分率=0.03-370,000x=11,100

Answer: Paul will make an $11,100 commission on the house.
::回答:保罗会为这栋房子提供11,100美元的佣金。

Fees
::收费费

Percentage based fees are a common practice for architects and general contractors. A general contractor is someone who organizes and executes a construction project. Many contractors will charge a client the cost of doing the job plus a percentage of the cost to account for profit.
::建筑师和一般承包商通常采用按百分比计费的做法,总承包商是指组织和执行建筑项目的人,许多承包商将向客户收取工作费用加上一定比例的费用以计利。

Example
::示例示例示例示例

A general contractor is hired to build a house. The house will cost $250,000 to build, and the general contractor also includes a 24% fee for the cost to the overall price. How much will the person who hired the contractor have to pay?
::总承包商被雇用建造房屋,建造房屋的费用为250 000美元,而总承包商还包括总价24%的费用。雇用承包商的人要支付多少费用?

Since you are adding a percentage of the whole to the whole, you can use one of the methods discussed earlier in Activity 1. You can either find the part and add the fee to the whole, or you can find 100% + 24% = 124% of the cost of building the house.
::由于您在整体中增加了一个百分比,您可以使用活动1中早些时候讨论过的方法之一,您可以找到部件,并将费用加到整体,或者您可以找到100%+24%=建造房屋费用的124%。

For this problem , use the first method: find the fee and then add it to the cost using $\begin{aligned} part & = percent \cdot whole \end{aligned}$
::为此问题,请使用第一种方法:找出费用,然后使用部分=全百分数将其加到成本中。

Part: x
::部分:xx

Percent: 24% = 0.24
::百分比:24%=0.24

Whole: 250,000
::整个:250 000

$\begin{aligned} part & = percent \cdot whole \\ x & = 0.24 \cdot 250, 000 \\ x & = 60, 000 \end{aligned}$
::部分=百分数=0.24 250 000x=60 000

Answer: The client will have to pay $250,000 + $60,000 = $310,000.
::答复:客户必须支付250 000美元+60 000美元=310 000美元。

Discussion Question
::讨论问题

How else could the question above be solved?
::除此之外,如何解决上述问题?

Big Tipper
::大提示器

It is likely that at some point in your life, you have been to a restaurant where a tip was given to a waiter. This occurrence is common and many people struggle with the percent-based math involved in giving a tip.
::在你生命的某个时刻,你可能去过一家餐馆,那里向服务员提供小费。这种情况很常见,许多人在提供小费时,都苦苦挣扎于以百分数为基础的数学。

The idea of tipping dates all the way back to England in the 1500s when servants were given coins as a gesture of goodwill. Since then, the practice of tipping has spread globally and is done as a gesture of gratitude for hard work. Tips in the restaurant industry are commonly based on a percent of the bill. This percent ranges from about 15% to 20% of the bill and is added on to the bill.
::1500年代,当佣人得到硬币作为善意的表示时,小费日期的想法就一直追溯到英国。从那时起,小费的做法就遍及全球,是对辛勤工作的一种感谢。餐馆业的提示通常以法案的1%为基础。这一比例从法案的15%到20%不等,并被添加到法案中。

Example
::示例示例示例示例

You receive a bill from your favorite restaurant for $30. How much should you tip if you plan to tip 20%?
::你从你最喜欢的餐厅收到30美元的帐单。如果打算支付20%,你应该给多少小费?

Since you want to find the value of the tip, you need to find 20% of $30. You can use the equation $\begin{aligned} part = percent \cdot whole \end{aligned}$ to do this.
::由于您想要找到小费的值, 您需要找到 30 美元的 20% 。您可以使用方程式 = 百分率。

Part: $\begin{aligned} x \end{aligned}$
::部分:xx

Percent: 20% = 0.2
::百分比:20%=0.2%

Whole: 30
::整个:30

$\begin{aligned} part & = percent \cdot whole \\ x & = 0.2 \cdot 30 \\ x & = 6 \end{aligned}$
::部分=百分数=0.2=0.2=30x=6

Answer: The tip will be $6. This brings the total bill to $36.
::答复:小费为6美元,使帐单总额达到36美元。

Big Tipper Continued
::大提示器继续

There are many strategies for finding a tip. Many people use a calculator to multiply 0.20 by the bill, while some can use strategies to find the tip in their head. For example, s ince 20% is $\begin{aligned} \frac{1}{5} \end{aligned}$ as a fraction multiplying $\begin{aligned} \frac{1}{5} \end{aligned}$ by the bill has the same effect as dividing the bill by 5. However, this strategy can be hard to do in your head if the bill is large.
::有很多方法可以找到小费。许多人用计算器按法案乘以0.20, 而有些人则用计算器在他们的头上找到小费。例如,由于20%是小费,15是小费,15是小费,因此,法案除以5具有同样的效果。然而,如果法案是大的,那么,这个战略在你的脑中可能很难做到。

An even easier strategy involves using the idea that $\begin{aligned} 20 % = 10 % \cdot 2 \end{aligned}$ . Since 10% is $\begin{aligned} \frac{1}{10} \end{aligned}$ as a fraction, multiplying the bill by 10% has the same effect as dividing the bill by 10. Recall that to divide a number by 10, move the decimal one place to the left. For example, if your bill was $30.00, you can find 10% by moving the decimal place to get $3.00. Then, double this to find 20%, which is $6.00. Notice that this is the same value you found using the formula earlier in this activity.
::更简单的策略是使用20102的理念。由于10%是110分之一, 将帐单乘以10%具有与将帐单除以10相同的效果。提醒大家注意, 要将数字除以10, 将小数点移到左边一个位子。例如, 如果您的帐单是30.00, 您可以通过移动小数点获得 $3.00 来找到10%。然后, 翻一番来找到 20%, 也就是$6. 00。请注意, 这与您在这项活动中先前使用公式找到的值相同。

Example
::示例示例示例示例

Find a 20% tip for a bill of $45.82 using the previously described strategy.
::在45.82美元的帐单上使用前述策略找出20%的线索

Move the decimal one place to the left : 4.582
::将小数点后一位移到左边:4.582

Double it: 4.582 x 2 = 9.164
::双倍:4.582x2=9.164

Round to the nearest cent: 9.164 ≈ 9.16
::圆到最近的百分数: 9.164 9.16

Answer: The tip will be $9.16.
::答复:小费为9.16美元。

A 20% tip on $45.82 will bring the total bill to $54.98. Keep in mind that you are not restricted to tip an exact percentage. I t would be courteous to add in that extra two cents to make it an even $55.
::45.82的20%小费会让帐单总额达到54.98美元。请记住, 您并不局限于提示一个准确的百分比。如果在帐单中加上两美分, 使其达到甚至55美元, 将会是礼貌的。

Use the interactive below to practice calculating tip.
::使用下面的交互功能来练习计算小费。

INTERACTIVE

Tip

Put a tip in the input box. Aim for a tip that is around 20%.
::在输入框中放一个提示。瞄准一个大约20%的提示。

Click the "Check" button to check your answer.
::单击“ 检查” 按钮来检查您的回答。

Click the "New Amount" button to try a new bill.
::单击“ 新数额” 按钮尝试新帐单。

Summary

The formula $\begin{aligned} percent = \frac{p a r t}{w h o l e} \end{aligned}$ can be used to solve problems involving tipping, commission, and tax.
::公式百分数=整个部分可以用来解决涉及小费、佣金和税收的问题。

Section outline

General

解决涉及税务、委员会和收费的问题

Sales Tax ::销售销售税

Commission ::贸委员会委员会委员会,委员会

Fees ::收费费

Big Tipper ::大提示器

Big Tipper Continued ::大提示器继续

Sales Tax
::销售销售税

Commission
::贸委员会委员会委员会,委员会

Fees
::收费费

Big Tipper
::大提示器

Big Tipper Continued
::大提示器继续