6.13%求底“b”的百分比方程

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  %求底“b”的百分比方程

  

  [Figure 1]

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  A digital camera and SD card are bundle priced at $65.98. This price represents a 30% discount off the price of buying the digital camera and SD card separately. If you bought the digital camera and SD card separately instead of bundled, how much would you pay?
  ::数字相机和SD卡以65.98美元的价格被捆绑。这个价格代表了对单独购买数码相机和SD卡价格的30%的折扣。如果你单独购买数码相机和SD卡而不是捆绑,你会付多少钱?

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  In this concept, you will learn how to use the percent  equation  to find the base,  $\begin{array}{r}b\end{array}$ .
  ::在这个概念中,你会学会如何使用百分数方程来找到基数,b。

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  Using the Percent Equation to Find the Base
  ::使用百分数来寻找基地

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  When you know the percent and the amount, you can use the percent equation to find the base,  $\begin{array}{r}b\end{array}$ .
  ::当您知道百分比和数量时, 您可以使用百分比方程来找到基数, b 。

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  Let’s look at how to apply the percent equation to this problem.
  ::让我们来看看如何将百分率方程式应用到这个问题上。

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  3 is 50% of what number?
  ::3是多少数字的50%?

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  First, the words “of what number” let you know that you are looking for the base.
  ::首先,“数字”一词应让大家知道,你们正在寻找基地。

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  Next, insert the other given information into our equation. First, let’s change the percent to a decimal.
  ::接下来,在我们的方程中插入其他给定信息。首先,让我们将百分比修改为小数点。

  $$\begin{array}{r}p=50\mathrm{\%}=0.50\end{array}$$

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  Then, work on the percent equation, filling in the given values.
  ::然后研究百分比方程 填充给定值

  $$\begin{array}{r}\begin{array}{rcl}a& =& p\times b\\ 3& =& 0.50b\end{array}\end{array}$$

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  Next, use the  inverse operation  and solve for  $\begin{array}{r}b\end{array}$ .
  ::下一步,使用反向操作并解决 b 。

  $$\begin{array}{r}\begin{array}{rcl}\frac{3}{0.5}& =& b\\ 6& =& b\end{array}\end{array}$$

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  The answer is 3 is 50% of 6.
  ::答案是3是6的50%。

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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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  9 is 75% of what number?
  ::9是多少数字的75%?

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  First, let’s change 75% to a decimal.
  ::首先,让我们将75%改为小数点后一位。

  $$\begin{array}{r}75\mathrm{\%}=0.75\end{array}$$

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  Next, let’s fill the given values into the equation.
  ::接下来,让我们将给定的值填入方程式。

  $$\begin{array}{r}9=0.75b\end{array}$$

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  Now you can solve for  $\begin{array}{r}b\end{array}$  using the inverse operation.
  ::现在您可以用反向操作解决 b 。

  $$\begin{array}{r}\begin{array}{rcl}\frac{9}{0.75}& =& b\\ 12& =& b\end{array}\end{array}$$

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  The answer is 9 is 75% of 12.
  ::答案是9是12分的75%。

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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 the bundled digital camera and SD card.
  ::早些时候,有人给了你一个问题 关于捆绑的数字相机 和SD卡。

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  It was priced at $65.98, which was 30% off the total cost of buying both items separately. If you bought the digital camera and SD card separately instead of bundled, how much would you pay?
  ::它的价格是65.98美元,是分开购买两件物品总成本的30%。如果你单独购买数码相机和SD卡而不是捆绑,你会付多少钱?

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  First, a 30% discount means that $65.98 is 70%  $\begin{array}{r}(100\mathrm{\%}-30\mathrm{\%})\end{array}$  of the cost of the two items separately.
  ::首先,30%的折扣意味着65.98美元是这两个项目费用的70%(100%-30%)。

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  Now, let’s change 70% to a decimal.
  ::现在,让我们将70%改为小数点后一位。

  $$\begin{array}{r}70\mathrm{\%}=0.70\end{array}$$

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  Next, let’s fill the given values into the equation.
  ::接下来,让我们将给定的值填入方程式。

  $$\begin{array}{r}65.98=0.70b\end{array}$$

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  Then you can solve for  $\begin{array}{r}b\end{array}$  using the inverse operation.
  ::然后您就可以用反向操作解决 b 。

  $$\begin{array}{r}\begin{array}{rcl}\frac{65.98}{0.70}& =& b\\ 94.26& =& b\end{array}\end{array}$$

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  The answer is the cost of buying the two items separately would be $94.26.
  ::答案是分别购买这两个项目的费用为94.26美元。

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  Example 2
  ::例2

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  The Cougars basketball team won 21 games. If that number is 70% of the games that the team played, how many games did the Cougars play?
  ::美洲狮篮球队赢得了21场比赛。如果这个数字是该球队所玩游戏的70%,美洲狮队玩了多少场比赛?

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  Think: 70% is the percent. 21 is the amount of games that they won. You want to find the base.
  ::想想:70%是百分比。 21是他们赢得的游戏数量。 您想要找到基础 。

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  First, take 70% and write it as a decimal.
  ::首先,取70%,然后写成小数点。

  $$\begin{array}{r}70\mathrm{\%}=0.70\end{array}$$

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  Next, write the given information into an equation and solve it using the inverse operation.
  ::下一步,将给定的信息写入方程式,然后使用反向操作解答它。

  $$\begin{array}{r}\begin{array}{rcl}21& =& 0.70b\\ \frac{21}{0.7}& =& b\\ 30& =& b\end{array}\end{array}$$

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  The answer is the team played 30 games in all.
  ::答案是球队总共打了30场比赛

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  Example 3
  ::例3

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  8 is 20% of what number?
  ::8%是多少的20%?

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  First, let’s change 20% to a decimal.
  ::首先,让我们将20%改为小数点后一位。

  $$\begin{array}{r}20\mathrm{\%}=0.20\end{array}$$

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  Next, let’s fill the given values into the equation.
  ::接下来,让我们将给定的值填入方程式。

  $$\begin{array}{r}8=0.20b\end{array}$$

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  Now you can solve for  $\begin{array}{r}b\end{array}$  using the inverse operation.
  ::现在您可以用反向操作解决 b 。

  $$\begin{array}{r}\begin{array}{rcl}\frac{8}{0.20}& =& b\\ 40& =& b\end{array}\end{array}$$

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  The answer is 8 is 20% of 40.
  ::答案是8是40分的20%

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  Example 4
  ::例4

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  15 is 30% of what number?
  ::15是多少数字的30%?

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  First, let’s change 30% to a decimal.
  ::首先,让我们将30%改为小数点后一位。

  $$\begin{array}{r}30\mathrm{\%}=0.30\end{array}$$

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  Next, let’s fill the given values into the equation.
  ::接下来,让我们将给定的值填入方程式。

  $$\begin{array}{r}15=0.30b\end{array}$$

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  Now you can solve for  $\begin{array}{r}b\end{array}$  using the inverse operation.
  ::现在您可以用反向操作解决 b 。

  $$\begin{array}{r}\begin{array}{rcl}\frac{15}{0.30}& =& b\\ 50& =& b\end{array}\end{array}$$

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  The answer is 15 is 30% of 50.
  ::答案是15是50分的30%

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  Example 5
  ::例5

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  22 is 40% of what number?
  ::22%是多少数字的40%?

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  First, let’s change 40% to a decimal.
  ::首先,让我们将40%改为小数点后一位。

  $$\begin{array}{r}40\mathrm{\%}=0.40\end{array}$$

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  Next, let’s fill the given values into the equation.
  ::接下来,让我们将给定的值填入方程式。

  $$\begin{array}{r}22=0.40b\end{array}$$

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  Now you can solve for  $\begin{array}{r}b\end{array}$  using the inverse operation.
  ::现在您可以用反向操作解决 b 。

  $$\begin{array}{r}\begin{array}{rcl}\frac{22}{0.40}& =& b\\ 55& =& b\end{array}\end{array}$$

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  The answer is 22 is 40% of 55.
  ::答案是22是55分的40%。

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  Review
  ::回顾

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  Use the percent equation to find each base. Round your answers to the nearest tenths when needed.
  ::使用百分数方程式查找每个基数。 需要时, 将您的答案转至最接近的十分之一 。

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  1. 5 is 10% of what number?
     ::5是多少数字的10%?
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  2. 15 is 30% of what number?
     ::15是多少数字的30%?
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  3. 18 is 20% of what number?
     ::18是什么数字的20%?
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  4. 12 is 50% of what number?
     ::12是多少数字的50%?
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  5. 15 is 40% of what number?
     ::15是多少数字的40%?
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  6. 14 is 20% of what number?
     ::14是什么数字的20%?
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  7. 80 is 25% of what number?
     ::80%是多少数字的25%?
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  8. 60 is 30% of what number?
     ::60%是多少数字的30%?
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  9. 45 is 40% of what number?
     ::45是多少数字的40%?
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  10. 16 is 25% of what number?
      ::16是多少数字的25%?
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  11. 60 is 18% of what number?
      ::60%是哪个数字的18%?
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  12. 25 is 30% of what number?
      ::25是多少数字的30%?
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  13. 21 is 15% of what number?
      ::21是什么数字的15%?
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  14. 55 is 10% of what number?
      ::55是什么数字的10%?

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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