6.7求底b的比例

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  求底b的比例

  

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  Kelsey wants to buy a new necklace for the school dance. She learns that her favorite store is having a one-day sale and has knocked down the price of all its necklaces to $9.95. The necklace Kelsey wants has been reduced by 47%. What is its non-sale price?
  ::Kelsey想为学校舞蹈买一条新项链。她知道她最喜欢的商店有一天的销售,把所有项链的价格都压到9.95美元。Kelsey想要的项链减少了47%。它的非销售价格是多少?

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  In this concept, you will learn to use cross products of proportions to find a base,  $\begin{array}{r}b\end{array}$ .
  ::在这个概念中,你将学会使用比例的交叉产品来寻找基准,b。

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  Using Proportions to Find Base, b
  ::使用比例来查找基准,b

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  There are many different ways to figure out a part of a whole, but one way is by using proportions.
  ::有很多不同的方法来找出整体的一部分, 但一种方法是使用比例。

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  Cross products can be used to solve for the base as well as the percent and the amount.
  ::交叉产品可用于解决基数以及百分比和数量问题。

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  When you see the phrase “Of what number?” you know that you are going to be solving for  $\begin{array}{r}b\end{array}$ , the base. You can then use the same  proportion  to solve for  $\begin{array}{r}b\end{array}$ .
  ::当您看到“什么数字?” 的短语时,您知道您将要解决 b, 基数。然后您可以使用相同的比例来解决 b 。

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  Let’s take a look at an example.
  ::让我们举个例子。

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  33 is 15% of what number?
  ::33是哪个数字的15%?

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  Remember that the number following the word “of” is the base. Since there is no number after the word “of”, you need to find the base  $\begin{array}{r}(b)\end{array}$ . 33 is the amount  $\begin{array}{r}(a)\end{array}$  and 15 is the percent  $\begin{array}{r}(p)\end{array}$ .
  ::记住“ of” 后的数字是基数。 因为“ of” 后没有数字, 您需要找到基数( b) 。 33 是数值( a ) , 15 是百分比( p ) 。

  $$\begin{array}{r}\begin{array}{rcl}\frac{a}{b}& =& \frac{p}{100}\\ \frac{33}{b}& =& \frac{15}{100}\\ 15b& =& 33(100)\\ 15b& =& 3,300\\ \frac{15b}{15}& =& \frac{3,300}{15}\\ b& =& 220\end{array}\end{array}$$

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  The answer is 33 is 15% of 220.
  ::答案是33是220的15%。

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  Let’s look at another example.
  ::让我们再看看另一个例子。

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  6 is 17% of what number. Round your answer to the nearest whole number?
  ::6是多少数字的17%。 将您的答复舍入到最近的整数 ?

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  To figure this out, let’s write a proportion.
  ::让我们来写一个比例。

  $$\begin{array}{r}\frac{6}{b}=\frac{17}{100}\end{array}$$

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  Next, use cross products to solve for  $\begin{array}{r}b\end{array}$ .
  ::接下来,使用交叉产品来解决b.

  $$\begin{array}{r}\begin{array}{rcl}17b& =& 6(100)\\ 17b& =& 600\\ b& =& 35.29\end{array}\end{array}$$

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  The answer is rounded to the nearest whole number, 6 is 17% of 35.
  ::答案四舍五入到最近的整数,6是35的17%。

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Kelsey and her new necklace.
  ::早些时候,你得到一个问题 关于凯尔和她的新项链。

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  For one day, the necklace she wants has been reduced to $9.95.
  ::有一天 她想要的项链 被缩减到9.95美元

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  The discount applied is 47%. What is the regular price of the necklace?
  ::使用的折扣是47% 项链的正常价格是多少?

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  First, figure out what you’re trying to find. If the discount is 47%, the sale price is  $\begin{array}{r}100\mathrm{\%}-47\mathrm{\%}\end{array}$  or 53% of the regular price. So you’re trying to find “$9.95 is 53% of what number?”
  ::首先,找出你想找到什么。 如果折扣是47 % , 销售价格是100% — — 47%或正常价格的53%。 因此,你试图找到“9.95美元是数字的53% ? ”

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  Now, let’s write a proportion.
  ::现在,让我们写一个比例。

  $$\begin{array}{r}\frac{9.95}{b}=\frac{53}{100}\end{array}$$

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  Next, use cross products to solve for  $\begin{array}{r}b\end{array}$ .
  ::接下来,使用交叉产品来解决b.

  $$\begin{array}{r}\begin{array}{rcl}53b& =& 9.95(100)\\ 53b& =& 995\\ b& =& \mathrm{\$}18.77\end{array}\end{array}$$

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  The answer is the regular price of the necklace is $18.77. 
  ::答案是项链的正常价格是18.77美元

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  Example 2
  ::例2

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  Six students in Miss Lang’s third period math class got A’s on their math test. This was 24% of the class.
  ::兰小姐第三学期数学班的6名学生在数学考试中获得了A级的成绩,占班级的24%。

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  How many students are in Miss Lang’s third period math class?
  ::兰小姐第三学期数学班有多少学生?

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  You can think of this problem as “6 is 24% of what number?” First, let’s set up the proportion.
  ::首先,让我们设定比例。

  $$\begin{array}{r}\frac{6}{b}=\frac{24}{100}\end{array}$$

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  Next, use cross products to solve for  $\begin{array}{r}b\end{array}$ .
  ::接下来,使用交叉产品来解决b.

  $$\begin{array}{r}\begin{array}{rcl}24b& =& 6(100)\\ 24b& =& 600\\ b& =& 600÷24\\ b& =& 25\end{array}\end{array}$$

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  The answer is there are 25 students in Miss Lang’s third period math class.
  ::答案是朗小姐第三期数学班有25名学生。

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  Example 3
  ::例3

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  6 is 25% of what number?
  ::6是多少数字的25%?

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  First, let’s write a proportion.
  ::首先,让我们写一个比例。

  $$\begin{array}{r}\frac{6}{b}=\frac{25}{100}\end{array}$$

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  Next, use cross products to solve for  $\begin{array}{r}b\end{array}$ .
  ::接下来,使用交叉产品来解决b.

  $$\begin{array}{r}\begin{array}{rcl}25b& =& 6(100)\\ 25b& =& 600\\ b& =& 24\end{array}\end{array}$$

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  The answer is 6 is 25% of 24.
  ::答案是6是24分的25%。

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  Example 4
  ::例4

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  12 is 8% of what number?
  ::12是什么数字的8%?

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  First, let’s write a proportion.
  ::首先,让我们写一个比例。

  $$\begin{array}{r}\frac{12}{b}=\frac{8}{100}\end{array}$$

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  Next, use cross products to solve for  $\begin{array}{r}b\end{array}$ .
  ::接下来,使用交叉产品来解决b.

  $$\begin{array}{r}\begin{array}{rcl}8b& =& 12(100)\\ 8b& =& 1,200\\ b& =& 150\end{array}\end{array}$$

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  The answer is that 12 is 8% of 150.
  ::答案是,12是150的8%。

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  Example 5
  ::例5

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  22 is 11% of what number?
  ::22%是多少的11%?

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  First, let’s write a proportion.
  ::首先,让我们写一个比例。

  $$\begin{array}{r}\frac{22}{b}=\frac{11}{100}\end{array}$$

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  Next, use cross products to solve for  $\begin{array}{r}b\end{array}$ .
  ::接下来,使用交叉产品来解决b.

  $$\begin{array}{r}\begin{array}{rcl}11b& =& 22(100)\\ 11b& =& 2,200\\ b& =& 200\end{array}\end{array}$$

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  The answer is that 22 is 11% of 200.
  ::答案是,22是200的11%。

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  Review
  ::回顾

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  Find each missing base.
  ::找到每个缺失的基地

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  1. 5 is 10% of what number?
     ::5是多少数字的10%?
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  2. 7 is 10% of what number?
     ::7是多少数字的10%?
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  3. 10 is 20% of what number?
     ::10%是什么数字的20%?
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  4. 16 is 40% of what number?
     ::16是多少的40%?
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  5. 8 is 25% of what number?
     ::8%是多少数字的25%?
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  6. 14 is 50% of what number?
     ::14是多少数字的50%?
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  7. 25 is 5% of what number?
     ::25是多少数字的5%?
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  8. 4 is 80% of what number?
     ::4是多少数字的80%?
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  9. 18 is 25% of what number?
     ::18是多少数字的25%?
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  10. 9 is 3% of what number?
      ::9%是多少的3%?
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  11. 15 is 20% of what number?
      ::15是多少数字的20%?
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  12. 15 is 12.5% of what number?
      ::15是多少数字的12.5%?
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  13. 22 is 5.5% of what number?
      ::22是多少的5.5%?

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  Review (Answers)
  ::回顾(答复)

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  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 。

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  Resources
  ::资源