节: 使用变化的百分率 | 5.12 使用变化的百分比

章节大纲

Bronze Gym’s membership is currently at 2,100 members. The owner, Jezzie, would like to increase this number by 15%. How many new members does she have to recruit? What will the new membership total be?
::青铜健身公司的成员目前为2,100名。老板杰齐希望将这一数字增加15 % 。她需要招募多少新成员? 新成员总数是多少?

In this concept, you will learn to use the percent of change to find new amounts.
::在这个概念中,你将学会使用变化的百分比来寻找新的数额。

Percent of Change
::变化百分比

You can find the percent of change if you know an original amount and how much it either increased or decreased. At times, however, you are given the or decrease and need to calculate a new amount.
::如果您知道一个初始数额,知道其增加或减少多少,您可以找到变化的百分比。但有时,您得到的或减少的,需要计算新的数额。

Let’s look at how you can calculate a new amount by using the percent of change.
::让我们看看如何使用变化的百分比来计算新的数额。

A restaurant manager has noticed an increase of 4% in the cost of utilities. In order to pay for the increased costs, he decides to increase prices by 4% as well. Not all items are priced the same. The chicken platter currently costs $5.99 and the steak platter cost $7.99. If the prices are increased by 4%, what will the new prices be?
::餐厅经理注意到水电费上涨了4%,为了支付上涨的费用,他决定同时提高4%的价格。不是所有物品的价格都一样。鸡盘目前花费5.99美元,牛排价格为7.99美元。如果价格上涨了4%,新价格会是什么?

First, calculate the new price of the chicken platter. You know that the original price is $5.99 and the price is going up 4%. Use the formula:
::首先,计算鸡盘的新价格。你知道原价格是5.99美元,价格将上升4%。使用公式:

$\begin{aligned} percent of change = \frac{amount of change}{original amount} \times 100 \end{aligned}$

::原数x100

Next, put in the amounts that you know.
::接下来,放进你所知道的金额里

$\begin{aligned} 4 % = \frac{amount of change}{5.99} \times 100 \end{aligned}$

::4 变动幅度 5.99×100

Then, divide by 100.
::然后,除以100

$\begin{aligned} \begin{array}{rcl} 4 % & = & \frac{amount of change}{5.99} \times 100 \\ \frac{4}{100} & = & \frac{\frac{amount of change}{5.99} \times 100}{100} \\ 0.04 & = & \frac{amount of change}{5.99} \end{array} \end{aligned}$

::4 变动额 5.99×1004100 = 变动额 5.99×1001000.04 = 变动额 5.99= 5.99×1000.04 = 变动额5.99

Then, multiply by 5.99.
::然后乘以5.99乘以5.99

$\begin{aligned} \begin{array}{rcl} 0.04 & = & \frac{amount of change}{5.99} \\ 0.04 \times 5.99 & = & \frac{amount of change}{5.99} \times 5.99 \\ amount of change & = & 0.2396 \end{array} \end{aligned}$

::004=变动额5.990.04×5.99=变动额5.99×5.99=变动额5.99×5.99=0.2396

The answer is 0.2396.
::答案是0.2396。

The chicken platter will increase in price by $\begin{aligned} 24 c \end{aligned}$ . The new price will be $6.23.
::鸡盘价格将上涨24美元。新的价格将为6.23美元。

Now, do the same calculations for the steak platter. The original price of the steak platter is $7.99 and it too will be increased by 4%.
::现在,对牛排盘做同样的计算。牛排盘的原价是7.99美元,它也会增加4%。

First, put in the amounts that you know.
::首先,把你知道的金额放进去

$\begin{aligned} 4 % = \frac{amount of change}{7.99} \times 100 \end{aligned}$

::4 变动幅度7.99×100

Then, divide by 100.
::然后,除以100

$\begin{aligned} \begin{array}{rcl} 4 % & = & \frac{amount of change}{7.99} \times 100 \\ \frac{4}{100} & = & \frac{\frac{amount of change}{7.99} \times 100}{100} \\ 0.04 & = & \frac{amount of change}{7.99} \end{array} \end{aligned}$

::=7.99×1004100=7.99×1000.04=7.99×1000.04=7.99=7.99×1000.04=7.99=7.99=7.99=7.99=7.99=7.99

Then, multiply by 7.99.
::然后乘以7.99乘以7.99

$\begin{aligned} \begin{array}{rcl} 0.04 & = & \frac{amount of change}{7.99} \\ 0.04 \times 7.99 & = & \frac{amount of change}{7.99} \times 7.99 \\ amount of change & = & 0.3196 \end{array} \end{aligned}$

::004=7.990.04×7.99=7.99×7.99=7.99×7.99=7.99=0.3196

The answer is 0.3196.
::答案是0.3196

The steak platter will increase in price by $\begin{aligned} 32 c \end{aligned}$ . The new price will be $8.31.
::牛排将涨价32c 新价为8.31美元

Let’s look at another question.
::让我们再看看另一个问题。

Find the new amount if 60 is decreased by 27%.
::如果60 减少27%, 则查找新金额。

First, use the formula to put in the amounts that you know.
::首先,使用公式来填入你所知道的金额。

$\begin{aligned} 27 % = \frac{amount of change}{60} \times 100 \end{aligned}$

::27 变动额60×100

Then, divide by 100.
::然后,除以100

$\begin{aligned} \begin{array}{rcl} 27 % & = & \frac{amount of change}{60} \times 100 \\ \frac{27}{100} & = & \frac{\frac{amount of change}{60} \times 100}{100} \\ 0.27 & = & \frac{amount of change}{60} \end{array} \end{aligned}$

::27°=60×10027100=60×1001000.27=变化量60×1001000.27=变化量60

Then, multiply by 60.
::然后乘以60乘以60

$\begin{aligned} \begin{array}{rcl} 0.27 & = & \frac{amount of change}{60} \\ 0.27 \times 60 & = & \frac{amount of change}{60} \times 60 \\ amount of change & = & 16.2 \end{array} \end{aligned}$

::0.27=变动额600.27x60=变动额60x60=16.2

The answer is 16.2.
::答案是16.2。

Since this is a decrease, the new amount would be:
::由于这一减少,新的数额将是:

$\begin{aligned} 60 - 16.2 = 43.8 \end{aligned}$

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Bronze Gym’s flagging membership.
::更早之前,

The gym currently has 2,100 members and Jezzie, the owner, wants to increase this number by 15%. How many new members does she need to recruit?
::体育馆目前有2,100名成员,业主Jezzie想将这一数字增加15%。她需要招募多少新成员?

First, use the formula to put in the amounts that you know.
::首先,使用公式来填入你所知道的金额。

$\begin{aligned} 15 % = \frac{amount of change}{2100} \times 100 \end{aligned}$

::15 千兆字节变化2100×100

Then, divide by 100.
::然后,除以100

$\begin{aligned} \begin{array}{rcl} 15 % & = & \frac{amount of change}{2100} \times 100 \\ \frac{15}{100} & = & \frac{\frac{amount of change}{2100} \times 100}{100} \\ 0.15 & = & \frac{amount of change}{2100} \end{array} \end{aligned}$

::152100×10015100=2100×1001000.15=2100×1001000.15=2100

Then, multiply by 2100.
::然后乘以2100乘以2100

$\begin{aligned} \begin{array}{rcl} 0.15 & = & \frac{amount of change}{2100} \\ 0.15 \times 2100 & = & \frac{amount of change}{2100} \times 2100 \\ amount of change & = & 315 \end{array} \end{aligned}$

::0.15=变化量21000.15×2100=变化量2100×2100=变化量2100×2100=变化量315

The answer is 315. Since this is an increase, the new amount would be $\begin{aligned} 2100 + 315 = 2415 \end{aligned}$ .
::答案是315. 由于这一增加,新数额将为2100+315=2415。

Therefore, Jezzie will need to recruit 315 more members to bring her total membership to 2415.
::因此,Jezzie需要再征聘315名成员,使成员总数达到2415人。

Example 2
::例2

The number of students participating in the chess club increased in one year. It started off with 35 students and had an increase of 55%. Figure out the new number of students in the chess club given this increase.
::参加象棋俱乐部的学生人数在一年中增加了一年,从35名学生开始,增加了55%。

First, use the formula to put in the amounts that you know.
::首先,使用公式来填入你所知道的金额。

$\begin{aligned} 55 % = \frac{amount of change}{35} \times 100 \end{aligned}$

::55个变动35×100

Then, divide by 100.
::然后,除以100

$\begin{aligned} \begin{array}{rcl} 55 % & = & \frac{amount of change}{35} \times 100 \\ \frac{55}{100} & = & \frac{\frac{amount of change}{35} \times 100}{100} \\ 0.55 & = & \frac{amount of change}{35} \end{array} \end{aligned}$

::5535×10055100=35×100100.55=变动35×100100.00。

Then, multiply by 35.
::然后乘以35乘以35

$\begin{aligned} \begin{array}{rcl} 0.55 & = & \frac{amount of change}{35} \\ 0.55 \times 35 & = & \frac{amount of change}{35} \times 35 \\ amount of change & = & 19.25 \end{array} \end{aligned}$

::0.55=变动数 350.55×35=变动数 35×35=变动数 35×35a=19.25

The answer is 19.25.
::答案是19.25。

Since this is an increase, the new amount would be:
::由于这一数额有所增加,新的数额将是:

$\begin{aligned} 35 + 19 = 54 \end{aligned}$

The chess club would have 54 students.
::象棋俱乐部将有54名学生。

Example 3
::例3

Find the new amount if 10 is increased by 18%.
::如果 10 增加 18%, 则查找新金额。

First, use the formula to put in the amounts that you know.
::首先,使用公式来填入你所知道的金额。

$\begin{aligned} 18 % = \frac{amount of change}{10} \times 100 \end{aligned}$

::18千兆瓦变化10×100

Then, divide by 100.
::然后,除以100

$\begin{aligned} \begin{array}{rcl} 18 % & = & \frac{amount of change}{10} \times 100 \\ \frac{18}{100} & = & \frac{\frac{amount of change}{10} \times 100}{100} \\ 0.18 & = & \frac{amount of change}{10} \end{array} \end{aligned}$

::18 =10×10018100 =10×1001000.18 = 10x1001000.18 = 10 change10

Then, multiply by 10.
::然后乘以10乘以10

$\begin{aligned} \begin{array}{rcl} 0.18 & = & \frac{amount of change}{10} \\ 0.18 \times 10 & = & \frac{amount of change}{10} \times 10 \\ amount of change & = & 1.8 \end{array} \end{aligned}$

::0.18=变动额100.18×10=变动额10×10=1.8

The answer is 1.8.
::答案是1.8。

Since this is an increase, the new amount would be:
::由于这一数额有所增加,新的数额将是:

$\begin{aligned} 10 + 1.8 = 11.8 \end{aligned}$

Example 4
::例4

Find the new amount if 16 is decreased by 20%.
::如果16 减少20%, 则查找新金额。

First, use the formula to put in the amounts that you know.
::首先,使用公式来填入你所知道的金额。

$\begin{aligned} 20 % = \frac{amount of change}{16} \times 100 \end{aligned}$

::20 个变动 16x100

Then, divide by 100.
::然后,除以100

$\begin{aligned} \begin{array}{rcl} 20 % & = & \frac{amount of change}{16} \times 100 \\ \frac{20}{100} & = & \frac{\frac{amount of change}{16} \times 100}{100} \\ 0.20 & = & \frac{amount of change}{16} \end{array} \end{aligned}$

::= 变化量16×10020100=变化量16×1001000.20=变化量16

Then, multiply by 16.
::然后乘以16乘以16

$\begin{aligned} \begin{array}{rcl} 0.20 & = & \frac{amount of change}{16} \\ 0.20 \times 16 & = & \frac{amount of change}{16} \times 16 \\ amount of change & = & 3.2 \end{array} \end{aligned}$

::0.20x16=变化量 16x16x16 变化量=3.2

The answer is 3.2.
::答案是3.2。

Since this is a decrease, the new amount would be
::由于这一减少,新的数额将是

$\begin{aligned} 16 - 3.2 = 12.8 \end{aligned}$

Example 5
::例5

Find the new amount if 250 is increase by 30%.
::如果250是增加30%,请查找新的金额。

First, use the formula to put in the amounts that you know.
::首先,使用公式来填入你所知道的金额。

$\begin{aligned} 30 % = \frac{amount of change}{250} \times 100 \end{aligned}$

::30 个变动 250×100

Then, divide by 100.
::然后,除以100

$\begin{aligned} \begin{array}{rcl} 30 % & = & \frac{amount of change}{250} \times 100 \\ \frac{30}{100} & = & \frac{\frac{amount of change}{250} \times 100}{100} \\ 0.30 & = & \frac{amount of change}{100} \end{array} \end{aligned}$

::30=250×10030100=250×1001000.30=变动100

Then, multiply by 250.
::然后乘以250

$\begin{aligned} \begin{array}{rcl} 0.30 & = & \frac{amount of change}{250} \\ 0.30 \times 250 & = & \frac{amount of change}{250} \times 250 \\ amount of change & = & 75 \end{array} \end{aligned}$

::0.30=变化2500.30×250=变化250×250=变化250×255=变化75

The answer is 75.
::答案是75

Since this is an increase, the new amount would be:
::由于这一数额有所增加,新的数额将是:

$\begin{aligned} 250 + 75 = 325 \end{aligned}$

Review
::回顾

Use percent to find the new amount. You may round to the nearest whole number when necessary.
::查找新数额的百分率使用百分比。必要时,您可以四舍五入到最近的整数。

82 increased by 90%
::82 增加90%,增加90%

64 decreased by 10%
::64 减少了10%

9 increased by 55%
::9 增加9 55%

25,470 decreased by 77%
::25 470人减少77%

75 increased by 10%
::75 增加10%,增加10%

33 decreased by 5%
::33下降了5%

99 increased by 15%
::99年增长15%

40 decreased by 8%
::40人减少了8%

56 increased by 25%
::56 增加25%,增加25%

900 decreased by 30%
::900人减少30%

800 increased by 23%
::800 800 增加23%

789 increased by 12%
::789人增加12%

880 decreased by 10%
::880人减少10%

450 increased by 45%
::450 450 增加45%

855 decreased by 18%
::855人减少18%

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

Percent of Change ::变化百分比

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

Percent of Change
::变化百分比

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