Solve problems about percentages

### 1.1. Knowledge to remember

**first. **__For example__: Van Tho primary school has 600 students, including 315 girls. Find the percentage of the total number of students and the number of students in the whole school.

The ratio of female students to the number of students in the whole school is 315 : 600

We have: 315 : 600 = 0.525

0.525 x 100 : 100 = 52.5 : 100 = 52.5%

So the ratio of the number of female students to the total number of students is 52.5%.

Usually we write the calculation as follows:

315 : 600 = 0.525 = 52.5%

*** To find the percentage of two numbers 315 and 600 we do the following:

- Find the quotient of 315 and 600.
- Multiply that quotient by 100 and add the % symbol to the right of the product found.

**2.** __Problem__: In 80kg of sea water, there are 2.8kg of salt. Find the percentage of salt in seawater.

Solution guide:

The percentage of salt in seawater is:

2.8 : 80 = 0.035

0.035 = 3.5%

Answer: 3.5%

__For example__: The number of female students in the whole school is 420 and accounts for 52.5% of the school’s students. How many students does that school have?

52.5% of the school’s students are 420.

1% of the school’s students are:

420 : 52.5 = 8 (student)

The number of students in the school or 100% of the students in the whole school is:

8 x 100 = 800 (students)

The above two steps can be written as:

420 : 52.5 x 100 = 800

Or 420 x 100 : 52.5 = 800

To find a number knowing that 52.5% of it is 420, we can divide 420 by 52.5 and multiply by 100, or multiply 420 by 100 and divide by 52.5.

4. __Problem__: Last year a factory built 1590 cars. The factory has reached 120% of the plan. According to the plan, how many cars does the factory plan to produce?

Solution:

The number of cars the factory intends to produce is:

1590 x 100 : 120 = 1325 (car)

Answer: 1325 cars

5. __For example__: A primary school has 800 students, of which 52.5% are girls. Calculate the number of female students in that school.

It can be understood that 100% of the whole school’s students are all of the school’s students, here 100% of the school’s students are 800. We have:

1% of the school’s students are:

800 : 100 – 8 (students)

The number of female students or 52.5% of the whole school’s students is:

8 x 52.5 = 420 (students)

The above two steps can be written as:

800 : 100 x 52.5 = 420

Or 800 x 52.5 : 100 = 420

Want to find 52.5% of 800 we can take 800 divided by 100 and then multiply by 52.5 or take 800 times 52.5 and then divide by 100

6. __Problem__: Savings interest rate is 0.5% per month. A depositor saves 1000 000 VND, Calculates the interest after one month.

Solution:

The profit after one month is:

1000000 : 100 x 0.5 = 5000 (VND)

Answer: 5000 VND

### 1.2. Solve textbook exercises page 75

**Lesson 1 Textbook page 75**

Write the following decimals as percentages (in the denominator):

0.57; 0.3; 0.234; 1.35.

Sample: 0.57 = 57%.

__Solution guide:__

0.3 = 30%; 0.234 = 23.4%; 1.35 = 135%

Lesson 2 Textbook page 75

Calculate the percentage of two numbers (in the denominator):

a) 19 and 30; b) 45 and 61; c) 1,2 and 26

Sample: a)19:30=0.6333…=63.33%

__Solution guide:__

b) 45:61=0.7377…=73.77%

c) 1,2:26=0.0461…=4.61%

Lesson 3 Textbook page 75

A class of students has 25 students, including 13 girls. What percentage of the class is the number of female students?

__Solution guide:__

The ratio of the number of girls to the number of students in the class is:

13 : 25 = 0.52

0.52 = 52%

Answer: 52%

### 1.3. Solve the exercises in the textbook Practice page 76

**Lesson 1 Textbook page 76**

Calculation (according to the form):

a) 27.5% + 38%; b) 30% – 16%;

c) 14.2% x 4; d) 216% : 8.

Sample: 6% + 15% = 21%; 112.5% - 13% = 99.5%;

14.2% x 3 = 42.6%; 60% : 5 = 12%.

*Solution guide:*

a) 27.5% + 38% = 65.5%

b) 30% – 16% = 14%

c) 14.2% x 4 = 56.8%

d) 216% : 8 = 27%

Lesson 2 Textbook page 76

According to the plan, last year Hoa An village had to plant 20ha of corn. By the end of September, Hoa An village had planted 18 hectares and by the end of the year it had grown 23.5 hectares of corn. Ask:

a) By the end of September, Hoa An village has accomplished what percentage of the whole year plan?

b) At the end of the year, how many percent has Hoa An village accomplished and by what percentage exceeds the plan for the whole year?

*Solution guide:*

a) Percentage of the plan for the whole year of Hoa An village that can be accomplished by the end of September is:

18 : 20 = 0.90 = 90%.

b) Compared with the plan, by the end of the year, Hoa An village has accomplished the percentage:

23.5 : 20 = 1,175 = 117.5%

Hoa An village has exceeded the plan, the percentage is:

117.5% – 100% = 17.5%

Answer: a) 90%

b) 117.5% and 17.5%.

Lesson 3 Textbook page 76

A person spends 42,000 dong of capital to buy vegetables. After selling all the vegetables, that person earns 52 500 VND. Ask:

a) What is the percentage of the capital from selling vegetables?

b) What percentage did that person make?

*Solution guide:*

Summary: Capital: 42 000 VND

Selling price: 52 500 VND

Sales = …% of capital

Interest: …%

a) Compared to the capital, the money from selling vegetables is equal to:

52 500 : 42 000 = 1.25 = 125%

b) Consider capital as 100%.

That person has earned a percentage of the capital that is:

125% – 100% = 25%

Answer: a) 125%;

b) 25%.

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