4.5 连接到现实世界局势的比例

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  连接到现实世界局势的比例

  

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  Robbie went to the store to buy hamburgers for the family barbeque. The hamburgers were on sale for $3.99 for 4 burgers. Robbie needed 22 burgers for the barbeque. How much money did he spend?
  ::罗比去商店买汉堡包给家里的烤肉。汉堡包卖了3.99美元,4个汉堡。罗比需要22个汉堡。他花了多少钱?

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  In this concept, you will learn how to use proportions in real-world situations.
  ::在这个概念中,你们将学会如何在现实世界中使用比例。

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  Proportions
  ::比例比例

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  Proportions can be found in many real-world situations. You use proportions for many situations that you may not even be aware of. Let’s take a look at a situation where a proportion can be used to solve a real-world dilemma.
  ::比例可以在许多现实世界的情况中找到。 您对许多你可能甚至不知道的情况使用比例。 让我们来看看一个比例可以用来解决现实世界困境的情况。

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  Amanda read 18 pages in 23 minutes. At this rate , how many pages will she read in 45 minutes?
  ::阿曼达在23分钟内读了18页 照这个速度,45分钟后她会读多少页?

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  First, write your proportion.
  ::首先,写下你的比例

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  $$\begin{array}{r}\frac{18}{23}=\frac{x}{45}\end{array}$$

  
  ::1823=x45

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  Next, cross multiply.
  ::下一个,交叉乘数。

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  $$\begin{array}{r}\begin{array}{rcl}\frac{18}{23}& =& \frac{x}{45}\\ 23x& =& 18\times 45\\ 23x& =& 810\end{array}\end{array}$$

  
  ::1823=x4523x=18x4523x=18x4523x=810

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  Then, solve for  $\begin{array}{r}x\end{array}$  by dividing both sides by 23.
  ::然后,通过将双方除以23来解决x问题。

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  $$\begin{array}{r}\begin{array}{rcl}23x& =& 810\\ \frac{23x}{23}& =& \frac{810}{23}\\ x& =& 35.217\end{array}\end{array}$$

  
  ::23x=81023x23=81023xx=35.217

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  The answer is 35.2.
  ::答案是35.2

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  Amanda will read 35 pages in 45 minutes.
  ::阿曼达会在45分钟后读35页

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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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  John ate three hot dogs in six minutes. At this rate, how many will he eat in twelve minutes?
  ::约翰在六分钟内吃了三只热狗

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  First, write your proportion.
  ::首先,写下你的比例

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  $$\begin{array}{r}\frac{3}{6}=\frac{x}{12}\end{array}$$

  
  ::36=x12

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  Next, cross multiply.
  ::下一个,交叉乘数。

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  $$\begin{array}{r}\begin{array}{rcl}\frac{3}{6}& =& \frac{x}{12}\\ 6x& =& 3\times 12\\ 6x& =& 36\end{array}\end{array}$$

  
  ::36=126x=3x126x=36

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  Then, solve for $\begin{array}{r}x\end{array}$   by dividing both sides by 6.
  ::然后,通过将双方除以6来解决x问题。

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  $$\begin{array}{r}\begin{array}{rcl}6x& =& 36\\ \frac{6x}{6}& =& \frac{36}{6}\\ x& =& 6\end{array}\end{array}$$

  
  ::6x=366x6=366x=6

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  The answer is 6.
  ::答案是6个

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  John will eat 6 hotdogs in 12 minutes.
  ::约翰会在12分钟内吃6只热狗

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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  Robbie’s yummy purchase?
  ::先前, Robbie的美食购买给您带来了问题吗?

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  Robbie needs to figure out how much money he is going to spend on burgers. He needs 22 in total and it costs $3.99 for 4.
  ::罗比需要弄清楚他要花在汉堡上多少钱 他总共需要22块 4块要花3.99美元

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  First, write your proportion.
  ::首先,写下你的比例

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  $$\begin{array}{r}\frac{3.99}{4}=\frac{x}{22}\end{array}$$

  
  ::3.994=x22

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  Next, cross multiply.
  ::下一个,交叉乘数。

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  $$\begin{array}{r}\begin{array}{rcl}\frac{3.99}{4}& =& \frac{x}{22}\\ 4x& =& 22\times 3.99\\ 4x& =& 87.78\end{array}\end{array}$$

  
  ::3.994=x224x=22x3.994x=87.78

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  Then, solve for $\begin{array}{r}x\end{array}$  by dividing both sides by 4.
  ::然后,通过将两边除以4来解决 x 问题。

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  $$\begin{array}{r}\begin{array}{rcl}4x& =& 87.78\\ \frac{4x}{4}& =& \frac{87.78}{4}\\ x& =& 21.95\end{array}\end{array}$$

  
  ::4x=87.784x4=87.784x=21.95

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  The answer is 21.95.
  ::答案是21.95。

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  Robbie will spend $21.95 on the 22 burgers he needs.
  ::Robbie会花21.95美元 在他需要的22个汉堡包上

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  Example 2
  ::例2

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  Kelvin measured the distance from his door to the park. It is 1.5 miles. The distance from Kelvin’s house to the library is twice the distance from Kelvin’s door to the park. How far is it from Kelvin’s to the library?
  ::Kelvin测量了从门到公园的距离,距离是1.5英里,从Kelvin的家到图书馆的距离是从Kelvin的门到公园的两倍。 从Kelvin的门到图书馆还有多远?

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  First, write your proportion.
  ::首先,写下你的比例

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  $$\begin{array}{r}\frac{1}{1.5}=\frac{2}{x}\end{array}$$

  
  ::11.5=2x

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  Next, cross multiply.
  ::下一个,交叉乘数。

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  $$\begin{array}{r}\begin{array}{rcl}\frac{1}{1.5}& =& \frac{2}{x}\\ 1x& =& 1.5\times 2\\ x& =& 3\end{array}\end{array}$$

  
  ::11. 5= 2x1x=1.5x2x=3

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  The answer is 3.
  ::答案是3

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  It is three miles from Kelvin’s house to the library.
  ::离Kelvin的家只有三英里,

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  Example 3
  ::例3

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  Carmen ran one mile in 7 minutes. At this rate, how long will it take her to run 5 miles?
  ::卡门在7分钟内跑一英里 照这个速度,她要跑5英里还要多久?

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  First, write your proportion.
  ::首先,写下你的比例

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  $$\begin{array}{r}\frac{1}{7}=\frac{5}{x}\end{array}$$

  
  ::17=5x 17=5x

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  Next, cross multiply.
  ::下一个,交叉乘数。

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  $$\begin{array}{r}\begin{array}{rcl}\frac{1}{7}& =& \frac{5}{x}\\ 1x& =& 7\times 5\\ x& =& 35\end{array}\end{array}$$

  
  ::17=5x1x=7x5x=35

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  The answer is 35.
  ::答案是35岁

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  It will take 35 minutes to run 5 miles.
  ::需要35分钟才能跑5英里

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  Example 4
  ::例4

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  Jack bought 5 oranges for $3.99. What was the cost for one orange?
  ::杰克以3.99美元买了5个橙子 一个橙子要多少钱?

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  First, write your proportion.
  ::首先,写下你的比例

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  $$\begin{array}{r}\frac{3.99}{5}=\frac{x}{1}\end{array}$$

  
  ::3.995=x1

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  Next, cross multiply.
  ::下一个,交叉乘数。

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  $$\begin{array}{r}\begin{array}{rcl}\frac{3.99}{5}& =& \frac{x}{1}\\ 5x& =& 1\times 3.99\\ 5x& =& 3.99\end{array}\end{array}$$

  
  ::3.995=x15x=1x3.995x=3.999

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  Then, solve for $\begin{array}{r}x\end{array}$   by dividing both sides by 5.
  ::然后,通过将两边除以5来解决 x 问题。

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  $$\begin{array}{r}\begin{array}{rcl}5x& =& 3.99\\ \frac{5x}{5}& =& \frac{3.99}{5}\\ x& =& 0.798\end{array}\end{array}$$

  
  ::5x=3.995x5=3.995x=0.798

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  The answer is 0.798.
  ::答案是0.798。

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  One orange costs $0.80 or 80¢.
  ::一个橙色的费用为0.80美元或80美元。

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  Example 5
  ::例5

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  Jessie read three books in one week. At this rate, how many books will she read in 3 weeks?
  ::杰西在一周内读了三本书 照这个速度,她3周内会读几本书?

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  First, write your proportion.
  ::首先,写下你的比例

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  $$\begin{array}{r}\frac{3}{1}=\frac{x}{3}\end{array}$$

  
  ::31=x3 31=x3

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  Next, cross multiply.
  ::下一个,交叉乘数。

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  $$\begin{array}{r}\begin{array}{rcl}\frac{3}{1}& =& \frac{x}{3}\\ 1x& =& 3\times 3\\ x& =& 9\end{array}\end{array}$$

  The answer is 9.
  ::31=31x=3x3x3x9 回答是9

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  Jessie will read 9 books in 3 weeks.
  ::杰西将在3周内读9本书

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  Review
  ::回顾

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  Write a proportion and use equivalent ratios to solve the following problems.
  ::编写比例和采用等值比率来解决下列问题。

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  1. Marco makes $25 for every 2 hours he works. If he works for 12 hours, how much will he make?
  ::1. Marco每工作2小时挣25美元,如果工作12小时,能赚多少?

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  2. If Marco works for 6 hours, how much will he make?
  ::2. 如果Marco工作6小时,他能挣多少钱?

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  3. If Marco works for 4 hours, how much will he make?
  ::3. 如果Marco工作4小时,他能挣多少钱?

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  4. If Marco made $50 for every 2 hours he works, how much will he make in 10 hours?
  ::4. 如果Marco每工作两个小时就挣50美元,10小时能赚多少?

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  5. Corinne runs 2.8 miles in 30 minutes. If she runs for 150 minutes this week, how many miles will she have run?
  ::5. Corinne在30分钟内跑2.8英里,如果她本周跑150分钟,她能跑多少英里?

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  6. If she runs 300 minutes, how many miles will she run?
  ::6. 如果她跑300分钟,她能跑多少英里?

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  7. Adam drives 45 miles per hour. If he drives for 3.5 hours, how many miles will he have driven?
  ::7. 亚当每小时驾驶45英里,如果他驾驶3.5小时,将开多少英里?

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  8. If he drives 7 hours, how many miles will he have driven?
  ::8. 如果他开7小时车,他会开多少英里?

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  Use cross-multiplying and proportions to solve the following problems. Round to the nearest hundredths place where necessary.
  ::使用交叉倍数和比例来解决下列问题。 必要时, 圆到最近的一百个地方 。

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  9. Marni buys 2.5 pounds of grapefruit for $4.48. To the nearest cent, how much would 6 pounds of grapefruit cost?
  ::9. Marni以4.48美元购买2.5磅的葡萄油,对于最近的部分,6磅的葡萄油要花多少钱?

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  10. Sarah buys 3 pounds of bananas for $2.50. What is the cost for bananas per pound?
  ::10. Sarah以2.50美元购买3磅香蕉,每磅香蕉的费用是多少?

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  11. Glenn can make 8 flyers in 35 minutes. How long will it take him to make 50 flyers?
  ::11. Glenn在35分钟内可以做8份传单。他要多久才能做50份传单?

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  12. At this rate, how many flyers could Glenn make in 70 minutes?
  ::12. 照这个速度,Glenn在70分钟内能做多少传单?

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  13. How many in two hours?
  ::13,两小时有多少?

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  14. A store sells 21 pieces of clothing every 45 minutes. How long will it take the store to sell 100 pieces of clothing?
  ::14. 一家商店每45分钟出售21件衣服,卖100件衣服需要多长时间?

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  15. The basketball team scored 85 points in the last 2 games. How many points can they expect to score after 5 games?
  ::15. 篮球队在过去两场比赛中得85分,五场比赛后预期得分多少分?

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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 。