6.14 增长百分比

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  增长百分比

  

  [Figure 1]

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  On March 8, 2010, Cento Coffee Shop began charging $2.50 for its drip coffee. Prior to that date, the shop charged $2.25 for its drip coffee. What was the percent increase in the drip coffee’s cost on March 8, 2010?
  ::2010年3月8日,Cento咖啡店开始收取2.50美元的滴咖啡费。 在此之前,该店收取2.25美元的滴咖啡费。 2010年3月8日,滴咖啡成本增长了多少? 2010年3月8日,滴咖啡成本增长了多少?

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  In this concept, you will learn how to find the percent of increase.
  ::在这个概念中,你会学会 如何找到增长的百分率。

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  Finding Percent of Increase
  ::查找增加百分比

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  Sometimes, you will have a price that has been increased by a specific  amount . Other times you can observe that a price has increased over time. Past pricing is often thought of in this way. When you compare a past price and an increased current price, you can figure out the percent by which a price has increased. You call this percent the  percent of increase.
  ::有时,你将会看到一个价格已经以特定数量上涨。有时,你可以观察到一个价格随着时间推移而上涨。过去的价格常常被这样看待。比较过去的价格和不断上涨的当期价格,你可以找出价格上涨的百分率。你把这个百分比称为增长的百分率。

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  The  percent of increase  from one amount to another is the ratio of the amount of increase to the original amount.
  ::从一个数额到另一个数额增加的百分比是增加数额与原数额的比率。

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  To find the percent of increase, follow these steps.
  ::为了找到增长的百分率, 遵循这些步骤 。

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  First, find the amount of increase by subtracting the original price from the new price.
  ::首先,通过从新价格中减去原价来找到增加额。

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  Next, write a fraction in which the  numerator  is the amount of increase and the  denominator  is the original amount.
  ::下一步,写一个分数,其中分子是增加的量,分母是原始的量。

  $$\begin{array}{r}\text{Percent of increase}=\frac{\text{Amount of Increase}}{\text{Original Amount}}\end{array}$$

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  Then, write the fraction as a percent.
  ::然后,将分数写成百分比。

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  Now let’s apply these steps.
  ::现在让我们运用这些步骤。

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  Find the percent of increase from 20 to 35.
  ::发现从20%增加到35 %的增幅。

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  First, subtract 20 from 35.
  ::首先,在35中减去20。

  $$\begin{array}{r}35-20=15\end{array}$$

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  Next, write the fraction:  $\begin{array}{r}\text{Percent of increase}=\frac{\text{Amount of Increase}}{\text{Original Amount}}=\frac{15}{20}\end{array}$
  ::下一步,写下分数:增加的百分比 = 增加数额 = 原数额 = 15 20

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  Then:
  ::然后:

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  One Way
  ::单行

  $$\begin{array}{r}\begin{array}{rcl}\frac{15}{20}& =& \frac{x}{100}\\ 20x& =& 1,500\\ \frac{\cancel{20}x}{\cancel{20}}& =& \frac{1,500}{20}\\ x& =& 75\end{array}\end{array}$$

  Another Way

  $$\begin{array}{rl}& \frac{15}{20}=\frac{15÷5}{20÷5}=\frac{3}{4}\\ & \stackrel{0.75}{4\overline{)3.00}}\leftarrow \text{Divide to}2\text{decimal places.}\\ & 0.75=75\mathrm{\%}\end{array}$$

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  The answer is the percent of increase from 20 to 35 is 75%.
  ::答案是,从20%到35的增幅是75%。

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  Notice that you could solve for the percent in two different ways. One was to use a  proportion  and the other was to simply  divide . Either way, you will get the same answer.
  ::注意您可以用两种不同的方式解答百分比。 一种是使用比例,另一种是简单地分割。 无论哪种方式, 您都会得到相同的答案 。

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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 Cento Coffee House.
  ::早些时候,有人给了你一个问题 关于半人马咖啡馆。

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  On March 8, 2010, the price of a drip coffee went from $2.25 to $2.50. What was the percent increase in the drip coffee’s cost?
  ::2010年3月8日,滴咖啡的价格从2.25美元上升到2.50美元。 滴咖啡成本增长多少?

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  First, figure out the amount of the increase by subtracting.
  ::首先,从中减去增加的数额。

  $$\begin{array}{r}2.50-2.25=0.25\end{array}$$

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  Next, divide this number by the original amount.
  ::接下来,将这个数字除以原来的数额。

  $$\begin{array}{r}0.25÷2.25=0.11\end{array}$$

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  Finally, convert the decimal to a percent.
  ::最后,将小数点转换为百分之一。

  $$\begin{array}{r}0.11=11\mathrm{\%}\end{array}$$

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  The answer is the price of the drip coffee increased by 11%.
  ::答案是滴咖啡的价格上涨11%。

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  Example 2
  ::例2

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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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  Find the percent of increase from 24 to 72.
  ::发现从24岁增加到72岁的百分比。

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  First, subtract 24 from 72.
  ::首先,从72中减去24。

  $$\begin{array}{r}72-24=48\end{array}$$

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  Next, write the fraction:  $\begin{array}{r}\text{Percent of increase}=\frac{\text{Amount of Increase}}{\text{Original Amount}}=\frac{48}{24}\end{array}$
  ::下一步,写下分数:增加的百分比 = 增加数额 = 原数额 = 48 24

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  Then:
  ::然后:

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  One Way
  ::单行

  $$\begin{array}{r}\begin{array}{rcl}\frac{48}{24}& =& \frac{x}{100}\\ 24x& =& 4,800\\ \frac{\cancel{24}x}{\cancel{24}}& =& \frac{4,800}{24}\\ x& =& 200\end{array}\end{array}$$

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  Another Way
  ::另一种方式

  $$\begin{array}{r}\begin{array}{rcl}\frac{48}{24}& =& \frac{48÷24}{24÷24}=\frac{2}{1}\\ 2& =& 200\mathrm{\%}\end{array}\end{array}$$

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  The answer is the percent increase from 24 to 72 is 200%.
  ::答案是,24%到72 %的增幅是200%。

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  Yes, sometimes the percent of increase can be greater than 100%!
  ::是的,有时增长的百分率会超过100%!

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  Example 3
  ::例3

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  Find the percent of increase from 45 to 50. You may  round  to the nearest whole percent when needed.
  ::发现45%到50的增长率的百分比, 必要时您可以圆到最接近的百分率。

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  First, subtract 45 from 50.
  ::首先,50减45。

  $$\begin{array}{r}50-45=5\end{array}$$

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  Next, write the fraction:  $\begin{array}{r}\text{Percent of increase}=\frac{\text{Amount of Increase}}{\text{Original Amount}}=\frac{5}{45}\end{array}$  
  ::下一步,写下分数:增加的百分比 = 增加数额 = 原数额 = 5 45

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  Then solve the proportion:
  ::然后解析比例 :

  $$\begin{array}{r}\begin{array}{rcl}\frac{5}{45}& =& \frac{x}{100}\\ 45x& =& 500\\ x& =& 11.11\end{array}\end{array}$$

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  The answer is rounded to the nearest whole percent, the percent increase from 45 to 50 is 11%.
  ::答案四舍五入到最接近的百分率,45%到50的增幅为11%。

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  Example 4
  ::例4

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  Find the percent of increase from $1.00 to $1.75. You may round to the nearest whole percent when needed.
  ::找到从1.00美元到1.75美元增长的百分之一。 需要时,您可以圆到最近的整百分数。

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  First, subtract 1.00 from 1.75.
  ::首先,从1.75中减去1.00。

  $$\begin{array}{r}1.75-1.00=0.75\end{array}$$

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  Next, write the fraction:  $\begin{array}{r}\text{Percent of increase}=\frac{\text{Amount of Increase}}{\text{Original Amount}}=\frac{0.75}{1.00}\end{array}$
  ::下一步,写入分数:增加的百分比 = 增加额 = 增加额 原数额 = 0.75 1.00

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  Then, divide:
  ::然后,分开:

  $$\begin{array}{r}\frac{0.75}{1.00}=0.75=75\mathrm{\%}\end{array}$$

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  The answer is the percent increase from $1.00 to $1.75 is 75%.
  ::答案是,从1.00美元增加到1.75美元的百分比增加75%。

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  Example 5
  ::例5

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  Find the percent of increase from 34 to 60. You may round to the nearest whole percent when needed.
  ::找到从34到60的增幅的百分比, 必要时您可以圆到最近的整百分率。

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  First, subtract 34 from 60.
  ::首先,从60中减去34。

  $$\begin{array}{r}60-34=26\end{array}$$

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  Next, write the fraction:  $\begin{array}{r}\text{Percent of increase}=\frac{\text{Amount of Increase}}{\text{Original Amount}}=\frac{26}{34}\end{array}$
  ::下一步,写下分数:增加的百分比 = 增加数额 = 原数额 = 26 34

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  Then, solve the proportion: 
  ::然后,解决比例问题:

  $$\begin{array}{r}\begin{array}{rcl}\frac{26}{34}& =& \frac{x}{100}\\ 34x& =& 2,600\\ x& =& 76.47\end{array}\end{array}$$

  The answer is rounded to the nearest whole percent, the percent increase from 34 to 60 is 76%.

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  Review
  ::回顾

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  Find the percent of increase given the original amount. Round your answer to the nearest tenths place if needed..
  ::查找根据原始数量增加的百分比。 如果需要, 将您的答复舍入到最近的十分位数 。

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  1. From 25 to 40
     ::25至40
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  2. From 15 to 30
     ::15至30
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  3. From 18 to 50
     ::18至50
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  4. From 22 to 80
     ::22至80
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  5. From 16 to 18
     ::16-18岁
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  6. From 3 to 10
     ::3至10 间
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  7. From 85 to 100
     ::85至100
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  8. From 75 to 90
     ::75至90
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  9. From 26 to 36
     ::26至36
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  10. From 100 to 125
      ::100至125
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  11. From 100 to 150
      ::100至150
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  12. From 125 to 175
      ::125至175
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  13. From 175 to 200
      ::175至200
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  14. From 200 to 225
      ::200至225
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  15. From 225 to 275
      ::225至275

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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