7.3 口头模式的单一变数公式

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  来自口头模式的单一变数公式

  

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  Kelvin has twice as many chickens in his chicken coop as Murray has in his. If Kelvin has 60 chickens in his coop, write an equation to represent $\begin{array}{r}c\end{array}$ , the number of chickens in Murray’s chicken coop.
  ::Kelvin的鸡舍比Murray的鸡舍多一倍。 如果Kelvin的鸡舍有60只鸡,那就写一个代表C的方程式,默里鸡舍的鸡数量。

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  In this concept, you will learn to write single variable equations from verbal models.
  ::在此概念中,您将学习从语言模型中写出单一变量方程式。

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  Writing Single Variable Equations from Verbal Models
  ::从口头模式中写入单一变数等量

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  Changing a word problem into an equation can often help you in solving the problem. Carefully read the question to determine if the equation has addition , subtraction , multiplication , or division .
  ::将单词问题转换成方程式通常可以帮助您解决问题。 仔细阅读问题以确定方程式是否添加、 减法、 乘法或除法 。

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  Here is an example.
  ::举一个例子。

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  Write “four times a number is twelve” as an equation.
  ::“一个数字的四倍是12”作为一个方程式。

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  First, let $\begin{array}{r}x\end{array}$  be “a number.”
  ::首先,让x成为“一个数字”。

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  Next, consider that the word “times” means you multiply.
  ::接下来,考虑一下,“时间”一词意味着你乘以乘法。

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  $$\begin{array}{r}4\text{ times }x\end{array}$$

  
  ::4乘4 xx 4 次

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  $$\begin{array}{r}4x\end{array}$$

  
  ::4x 4x

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  Then, consider that the word “is” means equals.
  ::那么,认为“是”一词的意思是等同的。

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  $$\begin{array}{r}4x\text{ is }12\end{array}$$

  
  ::4x12 4x12 4x12

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  The equation is $\begin{array}{r}4x=12\end{array}$ .
  ::方程式是4x=12

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  Here is another example.
  ::下面是另一个例子。

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  Write “seven less than a number is fourteen” as an equation.
  ::将“少于数字的七分之十四”作为一个等式写成。

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  First, let $\begin{array}{r}x\end{array}$  be “a number.”
  ::首先,让x成为“一个数字”。

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  $$\begin{array}{r}7\text{ less than }x\text{ is }14\end{array}$$

  
  ::7小于x14, 7小于x14

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  Next, consider that “less than” means subtraction, but be careful about the order .
  ::其次,认为“低于”是指减法,但要注意顺序。

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  $$\begin{array}{r}x-7\text{ is }14\end{array}$$

  
  ::x-7为 14

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  Then, consider that the word “is” means equals.
  ::那么,认为“是”一词的意思是等同的。

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  $$\begin{array}{r}x-7=14\end{array}$$

  
  ::x-7=14 x-7=14

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  The equation is $\begin{array}{r}x-7=14\end{array}$ .
  ::方程式是 x-7=14 。

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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 chicken coops.
  ::早些时候,有人给了你 鸡舍的问题。

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  Kelvin has 60 chickens, which is twice as many chickens as Murray has. How can Kelvin write a single variable equation to represent his number of chickens?
  ::Kelvin有60只鸡,是Murray的两倍。 Kelvin如何能写出一个能代表鸡数的变量方程式?

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  First, simplify the language.
  ::首先,简化语言。

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  Kelvin has 60 chickens and this is 2 times $\begin{array}{r}c\end{array}$ , the number of chickens Murray has.
  ::Kelvin有60只鸡 这是Murray的2倍C

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  Next, consider that “is” means equals, and “times” means multiplication.
  ::其次,认为“是”系指等值,“时间”是指乘法。

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  $$\begin{array}{r}\begin{array}{rcl}60& =& 2\times c\\ 60& =& 2c\end{array}\end{array}$$

  
  ::60=2xxc60=2c

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  The equation $\begin{array}{r}60=2c\end{array}$  represents the number of chickens in Murray’s coop.
  ::等式60=2c代表Murray的圈子里的鸡数量。

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  Example 2
  ::例2

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  Carrie made 3 liters of lemonade for a party. After the party, she had 0.5 liters of lemonade left. Write an equation to represent $\begin{array}{r}n\end{array}$ , the number of liters of lemonade that her guests drank.
  ::Carrie为派对做了3升柠檬水 派对后她还剩下0.5升柠檬水 写一个方程式代表n, 也就是她客人喝的柠檬水的公升数

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  Use a number, an operation sign, a variable, or an equal sign to represent each part of the problem. Since the question tells you how many liters of lemonade were left after the party, this will be a subtraction equation.
  ::使用数字、 操作符号、 变量或等号来代表问题的每一部分。 既然问题可以告诉您在派对后还剩下多少升柠檬水, 这将是减法方程 。

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  Carrie started with 3 liters, and $\begin{array}{r}n\end{array}$  is the number of liters that the guest drank. So, $\begin{array}{r}3-n\end{array}$  is how much lemonade there was after the party, 0.5 liters.
  ::Carrie从3升开始, N是客人喝的升数。所以, 3升是派对之后有多少柠檬水, 0.5升。

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  For this problem, it may help to write an equation in simplified words and then translate those words into an algebraic equation .
  ::对于这个问题,用简化的字句写出一个方程式,然后将这些字词转换成代数方程式,可能会有所帮助。

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  $$\begin{array}{r}\begin{array}{rcl}\text{(number of liters made)}-\text{(number of liters guests drank)}& =& \text{(number of liters left)}\\ 3-n& =& 0.5\end{array}\end{array}$$

  
  ::=(剩下的升数)3-n=0.5

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  The equation is  $\begin{array}{r}3-n=0.5\end{array}$ .
  ::方程式是3 -n=0.5

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  Example 3
  ::例3

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  Write an equation for the following phrase: six and a number is twenty.
  ::写出以下短语的方程: 6, 数字为 20 。

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  First, let $\begin{array}{r}x\end{array}$  be “a number.”
  ::首先,让x成为“一个数字”。

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  $$\begin{array}{r}6\text{ and }x\text{ is }20\end{array}$$

  
  ::6和x为 20

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  Next, consider that “and” means addition.
  ::其次,认为“和”意指添加。

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  $$\begin{array}{r}6+x\text{ is }20\end{array}$$

  
  ::6+x是20 6+x是20

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  Then, consider that the word “is” means equals.
  ::那么,认为“是”一词的意思是等同的。

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  $$\begin{array}{r}6+x=20\end{array}$$

  
  ::6+x=20 6+x=20

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  The equation is $\begin{array}{r}6+x=20\end{array}$ .
  ::方程式是6+x=20

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  Example 4
  ::例4

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  Write an equation for the following phrase: eighteen divided by a number is three.
  ::写出以下短语的方程: 十八除以一个数字为 3。

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  First, let $\begin{array}{r}x\end{array}$  be “a number.”
  ::首先,让x成为“一个数字”。

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  $$\begin{array}{r}18\text{ divided by }x\text{ is }3\end{array}$$

  
  ::18除以x为3

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  Next, you know this involves division.
  ::接下来,你知道这涉及"组织"

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  $$\begin{array}{r}\frac{18}{x}\text{ is }3\end{array}$$

  
  ::18x3 18x3 18x3

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  Then, consider that the word “is” means equals.
  ::那么,认为“是”一词的意思是等同的。

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  $$\begin{array}{r}\frac{18}{x}=3\end{array}$$

  
  ::18x=3 18x=3

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  The equation is $\begin{array}{r}\frac{18}{x}=3\end{array}$ .
  ::方程是18x=3

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  Example 5
  ::例5

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  Write an equation for the following phrase: five times a number is twenty-five.
  ::为以下短语写一个方程:数字的5倍为25。

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  First, let $\begin{array}{r}y\end{array}$  be “a number.”
  ::首先,让你们成为“一个数字”。

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  $$\begin{array}{r}5\times y\text{ is }25\end{array}$$

  
  
  ::5xy为 25

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  Next, consider that the word “times” means you multiply.
  ::接下来,考虑一下,“时间”一词意味着你乘以乘法。

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  $$\begin{array}{r}5y\text{ is }25\end{array}$$

  
  ::5Y是25,5Y是25

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  Then, consider that the word “is” means equals.
  ::那么,认为“是”一词的意思是等同的。

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  $$\begin{array}{r}5y=25\end{array}$$

  
  ::5y=25

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  The equation is $\begin{array}{r}5y=25\end{array}$ .
  ::方程式是5y=25

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  Review
  ::回顾

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  Write an equation for each verbal model.
  ::为每个口头模型写一个方程。

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  1. Ten times a number is thirty.
     ::10倍一个数字是30。
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  2. Five times a number is fifteen.
     ::5乘以1个数字是15。
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  3. A number and seven is eleven.
     ::A号和7号是11号
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  4. A number divided by three is twelve.
     ::数字除以3是12。
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  5. A number and eighteen is thirty.
     ::A号和18号是30号
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  6. A number divided by twelve is fourteen.
     ::以十二除以十二是十四
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  7. Seven times a number is forty-nine.
     ::7乘以一个数字是49
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  8. A number divided by thirteen is seven.
     ::数字除以13是7。
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  9. Eight times a number is equal to sixty-four.
     ::一个数字八倍等于六十四

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  Write an algebraic expression for each situation below.
  ::为以下每种情况写一个代数表达式。

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  10. Arturo has 8 fewer stickers in his collection than Julissa has in hers. Let $\begin{array}{r}j\end{array}$  represent the number of stickers in Julissa’s collection. Write an expression to represent the number of stickers in Arturo’s collection.
      ::Arturo收藏的贴纸比Julissa收藏的贴纸少8个。 让j代表Julissa收藏的贴纸数量。 写一个表达方式来代表Arturo收藏的贴纸数量。
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  11. Let $\begin{array}{r}c\end{array}$  represent the number of cookies on a plate. Three friends share all the cookies on the plate equally. Write an expression to represent the number of cookies each friend has after they are shared equally.
      ::c 代表一个盘子上的饼干数量。 三个朋友平分了盘子上的所有饼干。 写一个表达式来表示每个朋友平分之后的饼干数量 。
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  12. Carly is twice as old as her sister. Let $\begin{array}{r}s\end{array}$  represent her sister’s age in years. Write an expression to represent Carly’s age in years.
      ::Carly的年纪比她的姐姐大一倍。 让我们在年中代表她姐姐的年纪。 写一个表示Carly年龄的表达方式。
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  13. The length of a rectangle is 3 inches longer than its width. Let $\begin{array}{r}w\end{array}$  stand for the width in inches. Write an expression to represent the length in inches.
      ::矩形的长度比其宽度长3英寸。让 w 代表宽度的英寸。写一个表达式以表示长度的英寸。

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  Write an algebraic equation for each word problem below.
  ::为下面的每个字问题写一个代数方程。

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  14. The chorus teacher divides all the students in the chorus into 3 equal groups. Each of the groups has 6 students in it. Write an equation that could be used to represent $\begin{array}{r}n\end{array}$ , the total number of students in the chorus.
      ::合唱教师将合唱团中的所有学生分成三个平等组,每个组有6名学生。写一个可以用来代表合唱团中学生总数n的方程式。
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  15. Matt’s dog weighs 30 pounds. His dog weighs 20 pounds more than his cat. Write an equation that could be used to represent $\begin{array}{r}c\end{array}$ , the weight, in pounds, of Matt’s cat.
      ::马特的狗重30磅。 他的狗比他的猫重20磅。 写一个可以用来代表马特的猫的C(以磅计的重量)的方程式。

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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 。