课程： 5.7 使用百分数方程式查找 Part a

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选择节使用百分比等量来查找 Part a

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使用百分比等量来查找 Part a
Jordan received $85 from his aunts for his birthday. He wants to buy a new game for his computer. His mother told him he could spend no more than 28% of his money on a computer game. How much money can Jordan spend?
::约旦从姑姑那里收到85美元,用于他的生日。他想买一台新的电脑游戏。他的母亲告诉他,他可以在电脑游戏上花费他钱的28%。约旦能花多少钱?

In this concept, you will learn to use the percent equation to find part a.
::在这个概念中,你会学会使用百分数方程来找到一个部分。

Finding Part a
::找寻部分a

You can use the proportion $\begin{align*}\frac{a}{b} = \frac{p}{100}\end{align*}$ to solve for a percent. You can also solve by using an equation. In this concept, you will use a proportion to create a different kind of equation that will help you solve percent problems.
::您可以使用比例 ab=p100 来解答一个百分比。您也可以使用方程式解答一个百分比。在此概念中,您将使用一个比例来创建一种不同的方程式,帮助您解答百分比问题。

When you solve the proportion $\begin{align*}\frac{a}{b} = \frac{p}{100}\end{align*}$ , you cross multiply to find the missing variable . You can rearrange this formula so that you are solving for just the variable $\begin{align*}a\end{align*}$ .
::当您解析比例 ab=p100 时,要找到缺失的变量,要交叉乘数。您可以重新排列此公式,这样您就可以只解决变量a 。

$\begin{aligned} \begin{array}{rcl} \frac{a}{b} & = & \frac{p}{100} \\ b \times \frac{a}{b} & = & \frac{p}{100} \times b \\ a & = & \frac{p b}{100} \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{a}{b} &=& \frac{p}{100} \\ b\times\frac{a}{b} &=& \frac{p}{100} \times b\\ a &=& \frac{pb}{100} \\ \end{array}\end{align*}$ You could also say that $\begin{align*}a= \frac{pb}{100}\end{align*}$ is equal to $\begin{align*}a = 0.01 pb\end{align*}$ . As well, you could convert your percent directly into a decimal and therefore the formula becomes even simpler.
::ab=p100bxab=p100xbb=p100。您也可以说a=pb100等于a=0.01pb。同样,您也可以直接将百分比转换为十进制,因此公式变得更加简单。

Let’s look at an example.
::让我们举个例子。

What is 85% of 90?
::90%的85%是多少?

First, change the 85% into a decimal. You know that percent means that the denominator of the fraction is 100.
::首先,将85%修改为小数点。你知道,百分比意味着分数分母为100。

Therefore, $\begin{align*}85\% = 0.85\end{align*}$ .
::因此,850.85。

Next, multiply using the percent equation.
::下一个,乘以百分比方程。

$\begin{aligned} \begin{array}{rcl} a & = & 0.01 p b \\ a & = & 0.85 \times 90 \\ a & = & 76.5 \end{array} \end{aligned}$
$\begin{align*} \begin{array}{rcl} a &=& 0.01 pb \\ a &=& 0.85 \times 90 \\ a &=& 76.5 \\ \end{array}\end{align*}$ The answer is 76.5.
::a=0.01pba=0.85x90a=76.5 答案是76.5。

Let’s look at another example.
::让我们再看看另一个例子。

What is 7% of 900?
::900的7%是多少?

First, change the 7% into a decimal. You know that percent means that the denominator of the fraction is 100.
::首先,将7%修改为小数点。你知道,百分比意味着分数分母为100。

Therefore, $\begin{align*}7\% = 0.07\end{align*}$ .
::因此,70.07。

Next, multiply using the percent equation.
::下一个,乘以百分比方程。

$\begin{aligned} \begin{array}{rcl} a & = & 0.01 p b \\ a & = & 0.07 \times 900 \\ a & = & 63 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} a &=& 0.01 pb \\ a &=& 0.07 \times 900 \\ a &=& 63 \end{array}\end{align*}$ The answer is 63.
::a=0.01pba=0.07x900a=63 答案是63。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Jordan and his partial spending money.
::早些时候,你被问及约旦和他部分支出资金的问题。

Jordan has $85 from his birthday but cannot spend any more than 28% of it on his new computer game. How much can he spend?
::Jordan生日时有85美元,但不能花超过28%的钱去玩新的电脑游戏。他能花多少钱?

First, change the 28% into a decimal.
::首先,将28%改为小数点。

$\begin{aligned} 28 % = 0.28 \end{aligned}$
$\begin{align*}28\% = 0.28\end{align*}$

Next, multiply using the percent equation.
::下一个,乘以百分比方程。

$\begin{aligned} \begin{array}{rcl} a & = & 0.01 p b \\ a & = & 0.28 \times 85 \\ a & = & 23.8 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} a &=& 0.01 pb \\ a &=& 0.28 \times 85 \\ a &=& 23.8 \end{array}\end{align*}$ The answer is 23.8.
::a=0.01pba=0.28x85a=23.8 答案是23.8。

Therefore, Jordan can spend up to $23.80 on his new computer game.
::因此,约旦可以在他的新电脑游戏上花费高达23.80美元。

Example 2
::例2

What is 19% of 300?
::300的19%是多少?

First, change the 19% into a decimal.
::首先,将19%改为小数点。

$\begin{align*}19\% = 0.19\end{align*}$

Next, multiply using the percent equation.
::下一个,乘以百分比方程。

$\begin{aligned} \begin{array}{rcl} a & = & 0.01 p b \\ a & = & 0.19 \times 300 \\ a & = & 57 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} a &=& 0.01 pb \\ a &=& 0.19 \times 300 \\ a &=& 57 \end{array}\end{align*}$ The answer is 57.
::a=0.01pba=0.19x300a=57 答案是57。

Example 3
::例3

What is 22% of 100?
::百分之22%是多少?

First, change the 22% into a decimal.
::首先,将22%改为小数点。

$\begin{aligned} 22 % = 0.22 \end{aligned}$
$\begin{align*}22\% = 0.22\end{align*}$

Next, multiply using the percent equation.
::下一个,乘以百分比方程。

$\begin{aligned} \begin{array}{rcl} a & = & 0.01 p b \\ a & = & 0.22 \times 100 \\ a & = & 22 \end{array} \end{aligned}$
$\begin{align*} \begin{array}{rcl} a &=& 0.01 pb \\ a &=& 0.22 \times 100 \\ a &=& 22 \end{array}\end{align*}$

::a=0.01pba=0.22x100a=22

The answer is 22.

::答案是22。

Example 4
::例4

What is 8% of 57?
::57的8%是多少?

First, change the 8% into a decimal.
::首先,将8%改为小数点后。

$\begin{aligned} 8 % = 0.08 \end{aligned}$
$\begin{align*}8\% = 0.08\end{align*}$

Next, multiply using the percent equation.
::下一个,乘以百分比方程。

$\begin{aligned} \begin{array}{rcl} a & = & 0.01 p b \\ a & = & 0.08 \times 57 \\ a & = & 4.56 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} a &=& 0.01 pb \\ a &=& 0.08 \times 57 \\ a &=& 4.56 \end{array}\end{align*}$
::a=0.01pba=0.08x57a=4.56

The answer is 4.56.
::答案是4.56

Example 5
::例5

What is 17% of 80?
::80分之17%是多少?

First, change the 17% into a decimal.
::首先,将17%改为小数点。

$\begin{aligned} 17 % = 0.17 \end{aligned}$
$\begin{align*}17\% = 0.17\end{align*}$

Next, multiply using the percent equation.
::下一个,乘以百分比方程。

$\begin{aligned} \begin{array}{rcl} a & = & 0.01 p b \\ a & = & 0.17 \times 80 \\ a & = & 13.6 \end{array} \end{aligned}$
$\begin{align*} \begin{array}{rcl} a &=& 0.01 pb \\ a &=& 0.17 \times 80 \\ a &=& 13.6 \end{array}\end{align*}$ The answer is 13.6.
::a=0.01pba=0.17x80a=13.6 答案是13.6。

Review
::回顾

Solve each percent problem. Round your answers to the nearest tenth when necessary.
::解决每个百分率的问题。必要时, 请将答案转至最近的十分之一。

How much is 15% of 73?
::73的15%是多少?

What is 70% of 5?
::5分之70%是多少?

What is 3% of 4 million?
::400万的3%是多少?

What is 18% of 30?
::30分的18%是多少?

What is 22% of 56?
::56的22%是多少?

What is 19% of 300?
::300的19%是多少?

What is 21% of 45?
::45分之21%是多少?

What is 34% of 250?
::250的34%是多少?

What is 33% of 675?
::675分的33%是多少?

What is 3% of 700?
::700的3%是多少?

What is 11% of 955?
::955的11%是多少?

What is 14% of 55?
::55分的14%是多少?

What is 37% of 17?
::17的37%是多少?

What is 20% of 9?
::百分之二十是百分之二十是百分之九吗?

What is 2% of 18?
::18分的2%是多少?

Review (Answers)
::回顾(答复)

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。

Resources
::资源

章节大纲

常规

使用百分比等量来查找 Part a

Finding Part a ::找寻部分a

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

Review (Answers) ::回顾(答复)

Resources ::资源

Finding Part a
::找寻部分a

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

Review (Answers)
::回顾(答复)

Resources
::资源