Course: 1.6现实生活用语

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现实生活用语
Kate needs to read 2 books over summer vacation. She doesn't have the books yet so she's not sure how many pages are in each book. Kate doesn't want to wait until the last minute to read the books so she is planning to read the same number of pages each day of her summer vacation. If Kate's summer vacation is 72 days long, how can she write a variable expression to represent the number of pages she will need to read each day?
::Kate在暑假期间需要读两本书。她没有书,所以她不知道每本书有多少页。 Kate不想等到最后一分钟才读这些书,所以她计划每天暑假时读同样的页数。如果Kate的暑假为72天,她怎么能写一个变量表达方式来表示她每天需要读多少页数呢?

Here you will learn how to write variable expressions to represent real world situations.
::在此您将学习如何写入变量表达式, 以代表真实世界状况。

Writing Variable Expressions for Real-Life Situations
::真实生活中的写作变量表达式

A variable expression is a mathematical phrase that contains numbers, operations , and variables.
::变量表达式是一个包含数字、操作和变量的数学短语。

Here are some examples of variable expressions:
::以下是一些变量表达式的例子:

$\begin{aligned} 3 x + y \end{aligned}$
::3 x + y 3 x + y

$\begin{aligned} 10 r - x \end{aligned}$
::10 r- xx

$\begin{aligned} b^{3} + 2 \end{aligned}$
::b 3+2 b 3+2

$\begin{aligned} m x - 4 \end{aligned}$
::m x - 4 个

You can use a variable expression to describe a real world situation where one or more quantities have an unknown value or can change in value.
::您可以使用变量表达式来描述一个或一个以上数量值未知或值可能变化的真实世界状况。

To write a variable expression for a real world situation:
::写下真实世界状况的变数表达式:

Figure out which quantity in the situation is unknown and define a variable to represent the unknown quantity.
::找出情况中的未知数量,并定义一个变量以表示未知数量。

Write an expression using the variable to represent the situation. Look for key words to help you figure out what mathematical operations you should use.
::使用变量写一个表达式以表达当前情况。查找关键字可以帮助您了解您应该使用什么数学操作。

Here is an example.
::举一个例子。

Ralph is a baker who makes the same number of loaves of bread each day. He uses 5 cups of flour in each loaf of bread. Write an expression to represent the number of cups of flour he uses each day making bread.
::拉尔夫是一个面包师,每天做同样数量的面包。他每块面包都用五杯面粉。写一个表达式来表示他每天做面包的面粉杯数量。

First, decide on your variable. You don't know how many loaves of bread Ralph makes each day, but you know every day it is the same.
::首先,决定你的变数你不知道拉尔夫每天做多少面包

Let $\begin{aligned} l \end{aligned}$ equal the number of loaves of bread Ralph makes each day.
::让我和拉尔夫每天做的面包数量相等

Next, write a variable expression using $\begin{aligned} l \end{aligned}$ . For each of the $\begin{aligned} l \end{aligned}$ loaves of bread Ralph uses 5 cups of flour. This means he uses $\begin{aligned} 5 l \end{aligned}$ cups of flour to make $\begin{aligned} l \end{aligned}$ loaves of bread.
::接下来,请用 l 来写一个变量表达式。对于每个我喜欢面包的人来说,拉尔夫都用5杯面粉。这意味着他用5升面粉来做面包。

$\begin{aligned} 5 l \end{aligned}$

The answer is Ralph uses $\begin{aligned} 5 l \end{aligned}$ cups of flour each day making bread where $\begin{aligned} l \end{aligned}$ is the number of loaves of bread he bakes each day.
::答案是拉尔夫每天用5升面粉做面包,我就是每天做面包的数量

Here is another example.
::下面是另一个例子。

Consider again Ralph who makes the same number of loaves of bread each day. Last Friday he only sold half of the loaves that he made. Write an expression to represent the number of loaves he sold.
::再想想每天做同样数量面包面包的拉尔夫。上周五他只卖掉了一半面包。写一个表达方式来表示他卖掉的面包的数量。

First, decide on your variable. You can use the same variable as last time since you still don't know the number of loaves of bread Ralph makes each day.
::首先,决定你的变量。你可以使用与上次相同的变量,因为你仍然不知道拉尔夫每天做的面包面包数量。

Let $\begin{aligned} l \end{aligned}$ equal the number of loaves of bread Ralph makes each day.
::让我和拉尔夫每天做的面包数量相等

Next, write a variable expression using $\begin{aligned} l \end{aligned}$ . If last Friday he had $\begin{aligned} l \end{aligned}$ loaves of bread but only sold half of them, he sold $\begin{aligned} \frac{1}{2} l \end{aligned}$ or $\begin{aligned} \frac{l}{2} \end{aligned}$ loaves of bread.
::接下来,用 l 写一个变量表达式。如果上周五他有我爱的面包,但只卖了一半,他卖了12升或2磅面包。

$\begin{aligned} \frac{l}{2} \end{aligned}$

The answer is Ralph sold $\begin{aligned} \frac{l}{2} \end{aligned}$ loaves of bread last Friday where $\begin{aligned} l \end{aligned}$ is the number of loaves of bread he bakes each day.
::答案是拉尔夫上星期五卖了两块面包上面我就是他每天烤面包的数量

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Kate and her summer reading.
::早些时候,你得到一个问题关于凯特和她的暑期阅读。

She has to read two books over her 72-day summer vacation. Her plan is to read the same number of pages each day.
::在72天的暑假期间,她必须读两本书,她计划每天阅读同样数量的页数。

First, Kate should decide on her variables. She doesn't know the number of pages in either book, so she will need two variables.
::首先,凯特应该决定她的变数。她不知道两本书的页数,所以她需要两个变数。

Let $\begin{aligned} x \end{aligned}$ equal the number of pages in the first book.
::x 等于第一本书的页数。

Let $\begin{aligned} y \end{aligned}$ equal the number of pages in the second book.
::y 等于第二本书的页数。

Next, write a variable expression using $\begin{aligned} x \end{aligned}$ and $\begin{aligned} y \end{aligned}$ . In total Kate will have to read $\begin{aligned} x + y \end{aligned}$ pages. She is going to read the same number of pages each of the 72 days of vacation. This means she should divide the total number of pages by 72 to find out how many pages she needs to read each day. Her expression is
::接下来,使用 x 和 y 写一个变量表达式。 Kate 总共将必须读取 x + y 页面。她将会在72天的假期中每次读取相同的页数。这意味着她应该将总页数除以 72 , 以了解她每天需要读多少页。她的表达式是:

$\begin{aligned} \frac{x + y}{72} \end{aligned}$

The answer is Kate needs to read $\begin{aligned} \frac{x + y}{72} \end{aligned}$ pages each day if $\begin{aligned} x \end{aligned}$ is the number of pages in the first book and $\begin{aligned} y \end{aligned}$ is the number of pages in the second book.
::答案是 Kate 每天需要阅读 x + y 72 页, 如果 x 是第一本书的页数, y 是第二本书的页数。

Example 2
::例2

John runs the same number of miles each day. Write an expression to represent the number of miles John ran in June last year.
::约翰每天运行的英里数相同。写一个表达式来表示约翰去年六月运行的英里数。

First, decide on your variable. You don't know how many miles John runs each day, but you know every day it is the same.
::首先,决定你的变数。你不知道约翰每天跑多少英里。

Let $\begin{aligned} m \end{aligned}$ equal the number of miles John runs each day.
::和约翰每天跑的英里数相等

Next, write a variable expression using $\begin{aligned} m \end{aligned}$ . In one day John runs $\begin{aligned} m \end{aligned}$ miles. In 2 days John runs $\begin{aligned} 2 m \end{aligned}$ miles. The question asks for an expression that represents how many miles John ran in June. June is a month with 30 days. So your expression is
::接下来,请用 m 写一个变量表达式。一天, John 跑一英里。 2天, John 跑2米。问题要求用一个表达式表示John 6月份跑多少英里。 6月是一个月, 30天。因此, 您的表达式是:

$\begin{aligned} 30 m \end{aligned}$

The answer is John ran $\begin{aligned} 30 m \end{aligned}$ miles in June last year where $\begin{aligned} m \end{aligned}$ is the number of miles he runs each day.
::答案是约翰去年6月跑了30米在那里,米是他每天跑的英里数。

Example 3
::例3

Karen bakes the same number of cookies each day in her bakery. Write an expression to represent the total number of cookies Karen bakes in a week.
::Karen每天在面包店里做同样数量的饼干。写一个表达方式, 表示一周内Cookie Karen烤的总数。

First, decide on your variable. You don't know how many cookies Karen bakes each day, but you know every day it is the same.
::首先,决定你的变数。你不知道卡伦每天烤多少饼干,但你知道每天都是一样的。

Let $\begin{aligned} c \end{aligned}$ equal the number of cookies Karen bakes each day.
::与克伦每天烤饼干的数量相等。

Next, write a variable expression using $\begin{aligned} c \end{aligned}$ . In one day Karen bakes $\begin{aligned} c \end{aligned}$ cookies. In 2 days Karen bakes $\begin{aligned} 2 c \end{aligned}$ cookies. The question asks for an expression that represents the total number of cookies Karen bakes in a week. A week has 7 days. So your expression is
::接下来,请使用 c. 写一个变量表达式。一天, Karen 烤 c cookies。两天后, Karen 烤 2 c cookies。问题要求使用一个表达式表示一周内Cookie Karen 烤的总数。一周有7天。所以, 您的表达式是 :

$\begin{aligned} 7 c \end{aligned}$

The answer is Karen bakes $\begin{aligned} 7 c \end{aligned}$ cookies each week where $\begin{aligned} c \end{aligned}$ is the number of cookies she bakes each day.
::答案是凯伦每周烤7 c c cookies 每星期,C是她每天烤的饼干数量。

Example 4
::例4

Eden caught 14 fish and then ate some. Write an expression to represent the number of fish Eden has left.
::伊甸园捕捉了14条鱼,然后吃了一些。写一个表达方式来表示伊甸园已经离开的鱼的数量。

First, decide on your variable. You don't know how many fish Eden ate.
::首先,决定你的变数你不知道有多少鱼被伊甸园吃掉

Let $\begin{aligned} x \end{aligned}$ equal the number of fish Eden ate.
::让 x 等于鱼的份数 Eden 食用。

Next, write a variable expression using $\begin{aligned} x \end{aligned}$ . Eden started with 14 fish, but then ate some. This means she will end up with less fish than she started with. You need to subtract the number of fish she ate from the number she started with. Your expression is
::下一步,使用 x 写一个变量表达式。 Eden 以 14 条鱼开始, 但然后吃一些。这意味着她最后的鱼数量会比她开始的少。您需要从她开始的鱼数量中减去她所吃鱼的数量。您的表达式是 :

$\begin{aligned} 14 - x \end{aligned}$

The answer is Eden now has $\begin{aligned} 14 - x \end{aligned}$ fish where $\begin{aligned} x \end{aligned}$ is the number of fish Eden ate.
::答案是伊甸园现在有14 - x鱼,其中x是伊甸园食鱼的数量。

Example 5
::例5

Jessica reads the same number of books each month. Write an expression to represent the number of books Jessica reads in 2 years.
::杰西卡每个月读的书数相同,写一个表达方式来代表杰西卡两年后读的书数。

First, decide on your variable. You don't know how many books Jessica reads each month, but you know every month it is the same.
::你不知道Jessica每个月读多少本书但每个月都一样

Let $\begin{aligned} b \end{aligned}$ equal the number of books Jessica reads each month.
::b 与Jessica每月阅读的书数相等。

Next, write a variable expression using $\begin{aligned} b \end{aligned}$ . In one month Jessica reads $\begin{aligned} b \end{aligned}$ books. In 2 months Jessica reads $\begin{aligned} 2 b \end{aligned}$ books. The question asks for an expression that represents the total number of books Jessica reads in 2 years. There are 12 months in a year so there are 24 months in 2 years. So your expression is
::接下来,使用 b 写一个变量表达式。一个月后Jessica读了 b 书。 2个月后Jessica读了 2 b 书。问题要求表达Jessica 两年内读的书籍总数。一年中有12个月, 两年中有24个月。所以, 您的表达式是 :

$\begin{aligned} 24 b \end{aligned}$

The answer is Jessica reads $\begin{aligned} 24 b \end{aligned}$ books in 2 years where $\begin{aligned} b \end{aligned}$ is the number of books she reads each month.
::答案是杰西卡在两年内读了24本b书里面的b是她每月读的书数

Review
::回顾

Choose a variable to represent the number and write a variable expression for the following phrases.
::选择一个变量以代表数字,并为以下短语写入变量表达式。

19 decreased by a number
::减少19个,减少若干

4 less than the product of 4 and a number
::4 与4和数的产物小于4和数的产物小于4

30 more than a number
::30 以上一个数字

12 more than 3 times a number
::12乘以3乘以一个数字

A number divided by seven
::A除以7除以数

A number and seven divided by two
::A和7除以二除以一除以一除以二

16 times an unknown number
::16乘未知数字

A number divided by eight
::A除以八除以八

The quantity of a number and seven times two
::数量数乘以7乘以2

The quantity of a number and five divided by five
::数字和数量除以五除以五除以五除以五除以五除以五除以五除以五除以五除以五除以五除以五除以五除以五除以五除以五除以五除以五除以五除以五除以五除以五除以五除以五除以五

22 decreased by a number
::22 减少数22

Seventeen less than three times a number
::17次不到一个数字的三倍

Solve each problem.
::解决每一个问题。

A librarian has 4 times as many mystery books as romances. She lends out 12 mysteries. How many mysteries does she have now if she started with 15 romances?
::图书管理员拥有的神秘书籍是浪漫的4倍。她提供了12个谜。如果她以15个浪漫开始,她现在有多少个谜?

In Saturday’s basketball game, Roman scored a fourth of his teams points. If the team scored 48 points total, how many points did Roman score? Write an expression and solve.
::在周六的篮球比赛中,罗曼得分了四分之一的球队分数。如果球队得分总共48分,罗马得分多少分?写一个表达和解答。

At the garden show daffodil bulbs cost $3 and tulip bulbs cost $4. Latoya buys 7 tulip bulbs and twice as many daffodil bulbs as tulips bulbs. How much does she spend total? Write an expression and solve.
::拉托亚购买了7个郁金香灯泡,是郁金香灯泡的两倍。她总共花了多少钱?写一个表达式和解答。

Section outline

General

现实生活用语

Writing Variable Expressions for Real-Life Situations ::真实生活中的写作变量表达式

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Writing Variable Expressions for Real-Life Situations
::真实生活中的写作变量表达式

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾