以百分率解决问题

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You Must Pay the Rent
::你必须付房租

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When renting apartments, it is recommended that people do not pay more than 30% of their income for rent.  This guideline  originally came  from the  1960s when landlords weren’t allowed to charge a tenant more than 25% of their income. This percent increased to 30% in the 1980s. While this system  is no longer used to determine rent , the idea that an affordable house or apartment should not  be more than 30% of your income still lives on.
::租房时,建议人们不支付超过收入30%的房租。 这个准则最初来自1960年代,当时房东不能收取超过收入25%的房客。 在1980年代,这一比例上升到了30%。 虽然这个制度不再用于确定租金,但人们认为可负担的房屋或公寓不应超过收入的30%。

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When dealing with percents, there are always three things to focus on: the part, the whole, and the percent. If  you have two of these three values,  you can always find the third.

::当处理百分比时,总有三件事需要关注:部分、整体和百分比。如果这三点中有两个值,你总能找到第三点.%=整体。

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This relationship can be used to solve for a percent using the part and the whole. How can  you use this relationship to solve for the part or whole if  you have the other two values instead?
::此关系可以用此部分和整个来解答百分比 。 如果您有其它两个值, 您如何使用此关系解答此部分或整个 ?

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A Slice of Pie
::馅饼的切片

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A restaurant surveyed 450 customers asking them to rate their service on a scale from 1 to 5, with 1 being extremely dissatisfied and 5 being extremely satisfied. If 54 percent   of the customers rated their service a 5 , c an you think of a way to determine the number of  customers who were extremely satisfied with the service?
::一家餐馆对450名顾客进行了调查,要求他们从1到5级评分服务,其中1名顾客极不满意,5名顾客极为满意。 如果54%的顾客评定服务为5级,你能想个办法确定对服务极为满意的顾客人数吗?

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Thus far we have used tape diagrams to help solve problems like this. However, this can be  challenging when the percent is not a multiple of 10% or 5%. Use the interactive below to  try estimating the answer using a tape diagram.
::到目前为止,我们已经使用磁带图帮助解决这样的问题。 然而, 当百分比不是10%或5%的倍数时, 这可能具有挑战性。 使用下面的交互式图来尝试使用磁带图来估计答案 。

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Discussion Question
::讨论问题

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What is your estimate of how many customers were extremely satisfied with the service?
::你对有多少客户对这项服务极为满意的估计是多少?

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You  were  only able to get an estimate using tape diagrams.  In order to get a more exact answer,  you will need to use a formula . The formula comes from rearranging   the relationship  $\begin{array}{r}\text{percent}=\frac{\text{part}}{\text{whole}}.\end{array}$   By multiplying the whole to  the other side you get the following equation :
::您只能用磁带图表获得估计。 为了获得更准确的答案, 您需要使用公式。 公式来自重新排列关系百分比=整段。 通过将整段乘到另一侧, 您可以得到以下方程式 :

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::全百分率=部分

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This  formula gives us a one-step equation to solve for the part given the whole and percent.  Remember to  write the percent as a decimal or fraction .
::此公式给我们一个单步方程, 以解答给定的整数和百分数。 记住将百分比写为小数点或分数 。

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Example
::示例示例示例示例

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If  there are 450 total customers and 54% have given positive reviews, how many customers would you say like this restaurant?
::如果总共有450个顾客,54%的人做了正面的审查,那么,你说有多少个顾客喜欢这家餐厅?

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• Part = ?
  ::部分=?
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• Whole =  450
  ::整个=450
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• Percent = 54 % →  0.54
  ::百分比=54% = 0.54

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$\begin{array}{rl}\text{percent}\cdot \text{whole}& =\text{part}\\ 0.54\cdot 450& =\text{part}\\ 243& =\text{part}\end{array}$
::全百分数=0.54450 = part243= 部分

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Answer: 243 people were extremely satisfied with their service at the restaurant.
::答复:243人对其在餐馆的服务极为满意。

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Use the interactive below to find the missing data from the survey .
::使用下面的交互方式查找调查中缺失的数据。

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Discussion Question
::讨论问题

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Would it be possible to use the value of a slice that you have already found to find a missing slice value?
::您能否使用您已经找到的切片值来找到缺失的切片值 ?

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You Must Pay the Rent Continued
::您必须支付续租租金

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Jake is renting an apartment for $1,800 a month, and his monthly income is $5,625. What percent of Jake’s monthly income is his rent?
::Jake每月租1800美元的公寓, 他的月收入为5,625美元,

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B egin by using a tape diagram to estimate the percent of Jake’s monthly income that his rent is. 
::开始使用磁带图来估计Jake月收入中其房租的百分比。

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Discussion Question
::讨论问题

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What is your estimate of the percent of Jake’s monthly income that his rent is?
::你估计Jake月收入的百分之几是他的房租?

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Now that  you have an idea of what  you are trying to find, use your equation to get an exact answer.
::既然你已经知道自己在寻找什么, 用你的方程式来得到一个准确的答案。

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• Part = 1,800
  ::第1编=1 800
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• Whole = 5,625
  ::整个=5 625
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• Percent = ?
  ::百分率=?

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$\begin{array}{rl}\text{percent}\cdot \text{whole}& =\text{part}\\ x\cdot 5,625& =1,800\\ x& =1,800/5,625\\ x& =0.32\end{array}$
::全百分数=部分5 625=1 800x=1 800/5 625x=0.32

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When using the formula, write the percent as a decimal (which is why  the answer is often written as a decimal). To convert the answer to a percent,  you can move the decimal two places to the right.
::当使用公式时,将百分比写成小数点(这就是为什么答案往往以小数点写成小数点的原因)。要将答案转换为百分比,您可以将小数点后两个位移到右边。

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Answer: 32%
::答复:32%

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Use the interactive below to practice finding the whole when given the part and percent.
::使用下方的互动 来练习寻找整体 当给定部分和百分比时。

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Independently or as a group, choose a profession that you are interested in. Research the median monthly income or divide the median yearly income by twelve. Find thirty percent of the monthly income to see what rent they could afford. Look online to see which apartments they could afford.
::独立地或作为一个群体,选择您感兴趣的职业。 研究月收入中位数或者将年收入中位数除以12。 找到月收入的30%, 看看他们能付得起多少房租。 上网看看他们能付得起哪些公寓。