Review on finding the average

**Lesson 1 page 175: **Find the average of the following numbers

a) 137; 248 and 395. b) 348; 219; 560 and 725.

**Solution guide:**

- To calculate the average of multiple numbers, we calculate the sum of the numbers, and then divide that sum by the number of terms.

a) The average of these numbers is :

(137 + 248 + 395) : 3 = 260

b) The average of these numbers is :

(348 + 219 + 560 + 725) : 4 = 463

**Lesson 2 page 175: **In 5 consecutive years, the population of a ward has increased by 158 people, 147 people, 132 people, 103103 people, 95 people, respectively. In those 5 years, what is the average annual increase in population?

__Solution guide:__

- Calculating the average annual population growth, we divide the total population growth in 55 years by 55.

*Solution*

The number of people increasing in 5 years is:

158 + 147 + 132 + 103 + 95 = 635 (person)

The average number of people increasing each year is:

635 : 5 = 127 (person)

Answer: 127 people.

**Lesson 3 page 175: **Group One collected 36 notebooks. Group Two contributed 2 more books than Group One, but less than Group Three. On average, how many books does each group collect?

__Solution guide:__

- Number of books that Team Two can contribute = Number of books that Team One can collect +2 books.
- Number of books that group Three can collect = number of books that group Two can collect +2 books.
- Average number of books each group can contribute = Total number of books that three groups can collect: 3.

*Solution*

Group Two contributed the number of books as:

36 + 2 = 38 (book)

The number of books collected by Group Three is:

38 + 2 = 40 (book)

The average number of books each group can contribute is:

(36 + 38 + 40) : 3 = 38 (book)

Answer: 38 notebooks.

**Lesson 4 page 175: **A company moves pumps by car. For the first time, there are 3 cars, each car can carry 16 machines. Next time there are 5 cars, each car can carry 24 machines. On average, how many pumps can each car carry?

__Solution guide:__

- Number of engines 3 cars can carry for the first time = number of engines each car can carry for the first time × 3.
- Number of engines 5 cars can carry the first time = number of engines each car can carry next time × 5.
- Average number of engines each car can carry = total number of engines: total number of cars.

*Solution*

For the first time, 3 cars can carry the number of pumps:

16 × 3 = 48 (machine)

Next time 5 cars can carry the number of pumps is:

24 × 5 = 120 (machine)

The number of cars involved in carrying the pump is:

3 + 5 = 8 (car)

On average, each car can carry:

(48 + 120) : 8 = 21 (machine)

Answer: 21 pumps.

**Lesson 5, page 175: **The average of two numbers is 15. Find the two numbers, knowing that the larger number is twice the smaller number.

__Solution guide:__

- Sum of two numbers = average × 2.
- Find two numbers mathematically find two numbers when the sum and ratio of the two numbers are known.

*Solution*

The sum of the two numbers to find is:

15 × 2 = 30

We have a diagram:

According to the diagram, the total number of equal parts is :

2 + 1 = 3 (parts)

The small number is :

30 : 3 = 10

The big number is:

30−10 = 20

Answer: Large number: 20 ;

Number of babies: 10.

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