1.5 与现实世界问题连接变量表达式和操作顺序

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  与现实世界问题连接变量表达式和操作顺序

  

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  For her birthday, Sara received a ticket to go to the ballet to see The Nutcracker. Sara needs to figure out the cost for the tickets for her friends, but she isn’t sure exactly how many of her friends will be going, it could be three or four. The cost for one ticket is $35.00, and there is a $2.00 one-time fee for the ticket purchase. Sara needs to know the price if she buys three tickets and also if she buys four tickets. If Sara could write a variable expression to model her problem, how could she use it to figure out the cost of the tickets?
  ::她的生日,Sara收到一张去芭蕾舞团看《纽特克拉克》的票票。Sara需要为她的朋友弄清楚票价,但她不确定她的朋友会有多少票价,可能只有三到四张。 一张票价是35美元,购买票价是一次性2美元。Sara需要知道如果她买三张票和买四张票的价格。 如果Sara能写出一个可变的表达方式来模拟她的问题,她如何用它来计算票价?

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  In this concept, you will learn how to write a real world problem as a variable expression and how to evaluate the expression you have written using the .
  ::在此概念中, 您将学习如何将真实的世界问题写成变数表达式, 以及如何评价您使用该表达式所写的表达式 。

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  Variable Expressions and Order of Operations
  ::可变表达式和操作顺序

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  When you have an unknown quantity in a problem, you can use a variable to represent the unknown quantity and then use it to evaluate the problem. In the real world there are many scenarios to which you can apply what you know about variable expressions and evaluating them.
  ::当您遇到问题的数量未知时,您可以使用变量来代表未知的数量,然后用变量来评估问题。在现实世界中,有许多情景可以应用您对变量表达式的了解并进行评估。

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

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  Many events require that you purchase a ticket for admission. Tickets can have various prices if tickets are sold for adults, seniors or children. If you know the number and type of tickets being purchased and the price for each ticket, then you can figure out the total cost of the tickets.
  ::许多活动都要求您购买入场券。如果将机票卖给成人、老年人或儿童,机票价格可以不同。如果您知道购买的机票的数量和类型以及每张机票的价格,那么您可以计算出机票的总成本。

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  An amusement park charges each person eight dollars admission and one dollar and fifty-cents per ride. Write a variable expression to model this situation and use it to find the cost of admission and five ride tickets.
  ::一个游乐园向每个人收取8美元入场费和1美元和50美元。写一个可变的表达方式来模拟这种情况并利用它来寻找入场费和5张驾车票。

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  First, notice there is a cost of eight dollars for admission. You can start with the number $8.00
  ::首先,请注意入境费8美元。您可以从8美元开始。

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  Next, notice there is a charge of $1.50 per ride. Therefore you would have to add $\begin{array}{r}1.50x\end{array}$ , where $\begin{array}{r}x\end{array}$  is the number of rides, to the admission cost.
  ::接下来,请注意每程收费为1.50美元。因此,您必须在入场费中加上1.50 x,其中x为乘车次数。

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  Then, write a variable expression you can use to determine the cost of going to the amusement park and enjoying the rides.
  ::然后,写一个可变表达式,你可以用来确定去游乐园和享受游览的费用。

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  $$\begin{array}{r}\mathrm{\$}8.00+\mathrm{\$}1.50x\end{array}$$

  
  ::8.00+1.50美元x

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  Remember the variable  $\begin{array}{r}x\end{array}$  represents the number of rides. You can now evaluate the variable expression to find the cost of going to the amusement park and going on five rides.
  ::记住变量 x 代表乘车次数。 现在您可以对变量表达式进行评估, 以找到去游乐园和乘五轮车的费用 。

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  First substitute $\begin{array}{r}x=5\end{array}$  into $\begin{array}{r}8.00+1.50x\end{array}$  and write the new expression.
  ::第一替换 x=5 改为 8.00+1.50x, 并写新表达式 。

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  $$\begin{array}{r}8.00+1.50(5)\end{array}$$

  Use the order of operations to evaluate the expression.
  ::8.00+1.50(5) 使用操作顺序评价表达式。

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  Multiply:  $\begin{array}{r}1.50\times 5=7.50\end{array}$  to clear parenthesis and write the new expression. 
  ::乘以: 1.50x5=7.50 清除括号并写入新表达式。

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  $$\begin{array}{r}8.00+7.50\end{array}$$

  Next, add:  $\begin{array}{r}8.00+7.50=\mathrm{\$}15.50\end{array}$
  ::8.00+7.50 下加:8.00+7.50=15.50美元

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  The answer is $15.50.
  ::答案是15.50美元。

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  Let’s look at one more problem.
  ::让我们再看看另一个问题。

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  An ice cream cone costs $3.50 plus an additional $1.25 for chocolate dip. Write an expression to model the cost of two chocolate dip ice cream cones.
  ::冰淇淋甜甜圈要花3.50美元,外加1.25美元的巧克力酱。写一个表达式来模拟两个巧克力冰淇淋甜甜圈的成本。

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  You must write a numerical expression to model the real-world problem. Since there are two cones and two dips, use  $\begin{array}{r}2(3.50+1.25).\end{array}$
  ::您必须写一个数字表达式来模拟真实世界的问题。 因为有两个锥形和两个底片, 请使用 2( 2.3. 50+1. 25) 。

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  Now u se the order of operations to evaluate the expression.
  ::现在使用操作顺序来评价表达式 。

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  First, perform the indicated operation inside the parenthesis. 
  ::首先,在括号内执行指定的操作。

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  Next, add  $\begin{array}{r}3.50+1.25=4.75,\end{array}$  and write the new expression.
  ::下加3.50+1.25=4.75,并写下新表达式。

  $$\begin{array}{r}2(4.75)\end{array}$$

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  Then, multiply:  $\begin{array}{r}2\times 4.75=9.50\end{array}$
  ::乘以: 2x4.75=9.50

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  The answer is $9.50.
  ::答案是9.50美元。

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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 Sara and her ballet tickets. She needs to know the prices of  a three-ticket purchase  and a  four-ticket purchase. The price of one ticket is $35.00 and there is a $2.00 processing fee.
  ::早些时候,有人给了你萨拉和她的芭蕾舞票的问题。她需要知道三张票和四张票的价格。一张票的价格是35美元,手续费是2美元。

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  Write a variable expression t o determine the cost of the tickets .
  ::写一个可变表达式以确定票价 。

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  First, determine the variable. The variable will be the number of tickets purchased since that is the changeable amount. Let  $\begin{array}{r}x\end{array}$  be the variable.
  ::首先,确定变量。变量将是购买的机票数量,因为这是可修改的金额。让 x 成为变量。

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  Remember the price of $35.00 of must be included with the variable.
  ::记住35.00美元的价格必须包含在变量中。

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  Next, write this part of the expression $\begin{array}{r}35x\end{array}$ .   
  ::下一步,写入表达式35x的这一部分。

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  Then, include the onetime fee of $2.00 and write the variable expression.
  ::然后,包括一次性收费$2.00 并写下变量表达式。

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  The answer is  $\begin{array}{r}35x+2\end{array}$ .
  ::答案是 35x+2 。

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  Sara needs to use the variable expression and the order of operations to calculate the cost of 3 tickets and of 4 tickets.
  ::Sara需要使用可变表达式和操作顺序来计算3张罚单和4张罚单的费用。

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  First, substitute $\begin{array}{r}x=3\end{array}$  into $\begin{array}{r}35x+2\end{array}$  and write the new expression. 
  ::首先,将 x=3 替换为 35x+2, 并写入新表达式 。

  $$\begin{array}{r}35(3)+2\end{array}$$

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  Next, multiply:  $\begin{array}{r}35\times 3=105\end{array}$ to clear parenthesis and write the new expression. 
  ::下一个, 乘: 35x3=105 清除括号并写入新表达式 。

  $$\begin{array}{r}105+2\end{array}$$

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  Then, add: $\begin{array}{r}105+2=\mathrm{\$}107.00\end{array}$  
  ::然后加上:105+2=107.00美元

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  The answer is $107.00.
  ::答案是107美元

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  First, substitute $\begin{array}{r}x=4\end{array}$  into $\begin{array}{r}35x+2\end{array}$  and write the new expression. 
  ::首先,将 x=4 替换为 35x+2, 并写入新表达式 。

  $$\begin{array}{r}35(4)+2\end{array}$$

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  Next, multiply: $\begin{array}{r}35\times 3=140\end{array}$ to clear parenthesis and write the new expression.
  ::下一步,乘以:35x3=140来清除括号并写入新表达式。

  $$\begin{array}{r}140+2\end{array}$$

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  Then, add:  $\begin{array}{r}140+2=\mathrm{\$}142.00\end{array}$
  ::然后,加上:140+2=142.00美元

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  The answer is $142.00.
  ::答案是142美元

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  Sara will have to pay $107.00 for three tickets or $142.00 for four tickets.
  ::Sara得支付107.00美元的三张票 或者142.00美元的四张票

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  Example 2
  ::例2

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  Harriet is making an almond cake for her sister and needs some ingredients. When she arrives at the store, Harriet sees that a can of evaporated milk costs $1.99 and almonds are $3.99 per pound.
  ::哈丽特为姐姐做杏仁蛋糕,需要一些原料。 当她到达商店时,哈丽特看到一罐蒸发的牛奶成本为199美元,杏仁每磅3.99美元。

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  Write a variable expression to model this problem so that Harriet can calculate her total cost based on how many pounds of almonds she purchases. Use your variable expression to calculate the cost of her purchase if Harriet buys 3 pounds of almonds.
  ::写一个可变表达方式来模拟这个问题, 这样哈丽特就可以根据她购买的杏仁重量计算总成本。 使用您的可变表达方式来计算如果哈丽特购买3磅杏仁的话, 她的购买成本 。

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  First, determine the variable. The variable is going to be the number of pounds of almonds purchased since that is the changeable amount. Let  $\begin{array}{r}x\end{array}$  be the variable.
  ::首先,确定变量。变量将是购买的杏仁磅数,因为这是可变数额。让 x 成为变量。

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  Remember the price of $\begin{array}{r}\$3.99\end{array}$  must be included with the variable, write this part of the expression:  $\begin{array}{r}3.99x.\end{array}$
  ::记住3.99美元的价格必须包含在变量中,请写上表达式的这一部分:3.99x。

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  Harriet isn’t only purchasing almonds; she is also buying a can of evaporated milk. You must include this cost in your variable expression.
  ::哈丽特不仅购买杏仁,她还在购买一罐蒸发牛奶。 您必须在变量表达式中包括这一成本。

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  A dd the cost of the can of milk to the first part of your expression:
  ::将牛奶罐的成本加在您表达式的第一部分:

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  $$\begin{array}{r}3.99x+1.99\end{array}$$

  
  ::3.99x+1.99

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  The answer is  $\begin{array}{r}3.99x+\mathrm{1.99.}\end{array}$
  ::答案是3.99x+1.99。

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  First, substitute  $\begin{array}{r}x=3\text{into}3.99x+1.99\end{array}$  and write the new expression. 
  ::首先,将 x=3 替换为 3.99x+1.99, 并写入新表达式 。

  $$\begin{array}{r}3.99(3)+1.99\end{array}$$

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  Use the order of operations to evaluate the expression. 
  ::使用操作顺序来评价表达式。

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  Next, multiply:  $\begin{array}{r}3.99\times 3=11.97\end{array}$  to clear parenthesis and write the new expression.
  ::下一个, 乘以: 3.99x3=11.97 来清除括号并写入新表达式 。

  $$\begin{array}{r}11.97+1.99\end{array}$$

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  Then, add:  $\begin{array}{r}11.97+1.99=13.96\end{array}$
  ::然后加上:11.97+1.99=13.96

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  The answer is $13.96.
  ::答案是13.96美元。

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  Example 3
  ::例3

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  The cost for three people to fly from Sydney, Nova Scotia to Calgary, Alberta is $1535.75. The airline also applies an additional charge of $25.00 for each piece of checked luggage. Write an expression to model the problem.
  ::3个人从新斯科舍州悉尼飞往艾伯塔省卡尔加里(Calgary)的费用为1535.75美元,航空公司对每件检查行李也征收25.00美元的附加费用。

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  You must write a variable expression to model the problem.
  ::您必须写一个变量表达式来模拟问题 。

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  $\begin{array}{r}1535.75+25x\end{array}$ , where  $\begin{array}{r}x\end{array}$  represents the number of pieces of checked luggage.
  ::15.35.75+25x,x代表检查行李的数量。

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  Use your variable expression to figure out the total cost of the trip if 5 pieces of luggage are checked.
  ::如果检查了5件行李, 请使用您的变量表达式来计算旅行的总费用 。

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  First, substitute  $\begin{array}{r}x=5\end{array}$ into $\begin{array}{r}1535.75+25x\end{array}$  and write the new expression. 
  ::首先,将 x=5 改为 1535.75+25x,并写新表达式。

  $$\begin{array}{r}1535.75+25(5)\end{array}$$

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  Use the order of operations to evaluate the expression. 
  ::使用操作顺序来评价表达式。

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  Next, multiply:  $\begin{array}{r}25\times 5=125\end{array}$  to clear parenthesis and write the new expression.
  ::下一个, 乘: 25x5=125 清除括号并写入新表达式 。

  $$\begin{array}{r}1535.75+125\end{array}$$

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  Then, add:  $\begin{array}{r}1535.75+125=1660.75\end{array}$
  ::然后,加上:1535.75+125=1660.75

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  The answer is $1660.75. 
  ::答案是1660.75美元。

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  Example 4
  ::例4

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  Maria wants to sew a new valence for her living room window. The window used to be one pane of glass 5 feet wide but the new window has a center section that is 5 feet wide and two smaller sections on either side. The new sections are each 3 feet long. The length of the valence must be double the width of the window. Write a variable expression to model the problem.
  ::Maria想为她的客厅窗口缝合一个新的值。 窗口曾经是一整玻璃5英尺宽, 但新窗口的中间部分是5英尺宽, 双侧有两个小部分。 新区段每3英尺长。 新区段的长度必须是窗口宽度的两倍。 写一个变量表达式来模拟问题 。

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  $\begin{array}{r}3(5+2x),\end{array}$  where  $\begin{array}{r}x\end{array}$  represents the width of two smaller sections of the window.
  ::3(5+2x),其中 x 代表窗口两个较小部分的宽度。

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  Since the width of each of the smaller window sections is 3 three feet, evaluate the variable expression when  $\begin{array}{r}x=3\end{array}$ .
  ::由于每个较小窗口区域的宽度为3 3英尺, 当 x=3 时, 请对变量表达式进行评价 。

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  First, substitute the value  $\begin{array}{r}x=3\end{array}$  into the expression. 
  ::首先,将 x=3 值替换为表达式。

  $$\begin{array}{r}3(5+2(3))\end{array}$$

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  Use the order of operations to evaluate the variable expression.
  ::使用操作顺序来评价变量表达式。

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  Next, perform the operations inside the parenthesis.
  ::接下来,在括号内执行操作。

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  Multiply  $\begin{array}{r}2(3)=6,\end{array}$  and write the new expression.
  ::乘以 2(3)=6, 并写入新表达式 。

  $$\begin{array}{r}3(5+6)\end{array}$$

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  Next, add:  $\begin{array}{r}5+6=11\end{array}$   and write the new expression.
  ::下加: 5+6=11, 并写新表达式 。

  $$\begin{array}{r}3(11)\end{array}$$

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  Then, multiply $\begin{array}{r}3(11)=33\end{array}$  to clear the parenthesis.
  ::然后乘以3(11)=33来清除括号。

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  The answer is 33.
  ::答案是33岁

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  Review
  ::回顾

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  Write a variable expression for each situation described below.
  ::为下文所述每一种情况写一个可变表达式。

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  1. A pound of apples costs $4.50. Kelly isn’t sure how many pounds she is going to purchase.
     ::一磅苹果需要4.5美元。 Kelly不确定她要买多少磅。
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  2. Each touch down at a football game is worth 7 points. Write a variable expression where the number of touchdowns scored can change.
     ::每次在足球比赛中触地都值7点。 写一个变量表达式, 该表达式的触地得分数可以改变 。
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  3. Alex bought several bunches of bananas. Each bunch costs $.89. Write a variable expression to describe this situation.
     ::艾丽克丝买了几套香蕉 每套都花89美元 写一个可变的表达方式来描述这种情况
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  4. If an ice cream cone costs $3.20 and hot fudge is an additional $.45, write a variable expression where the number of ice cream cones can change.
     ::如果冰淇淋甜筒花费3.20美元,热软糖是额外的0.45美元,请写一个变式表达式,其中冰淇淋甜筒的数量可以改变。
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  5. A turkey costs $6.75 per pound. Write a variable expression where the weight of the turkey is the changeable amount.
     ::火鸡成本为每磅6.75美元。 写一个可变表达式, 火鸡的重量是可变数量 。
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  6. The car wash charges $15.00 per car. Write a variable expression that can be used to calculate the number of cars washed in one hour.
     ::洗车费为每辆车15美元。 写一个变量表达式, 可以用来计算一小时内洗车的车数 。
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  7. Kelly bought a pair of sneakers for $35.00. She also bought a pile of different laces. Each set of laces costs $3.00. Write a variable expression to show how Kelly could calculate her total cost.
     ::Kelly花了35美元买了一双运动鞋。她还买了一堆不同的鞋带。每套鞋带要花3美元。写一个可变表达式来显示 Kelly如何计算总成本。

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  Now go back to each of the variable expressions that you have written as the answers for the above questions and evaluate each expression using 4 as the given value for the variable. These are your answers for numbers 9–16.
  ::现在回到您写为上述问题答案的变量表达式中的每一变量表达式, 并使用给定值 4 来评估每个表达式。 这些是您对编号 9-16 的答案 。

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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 。