WORKSHEET ON AVERAGE WORD PROBLEMS

Problem 1 :

A student was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 5, 3, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x?

Problem 2 :

The average age of 30 kids is 9 years. If the teacher's age is included, the average age becomes 10 years. Find the teacher's age.

Problem 3 :

The average of 6 numbers is 8. What is the 7^th number, so that the average becomes 10?

Problem 4 :

David's average score in the last 9 tests is 80. What should be his score in his next test, so that his average score will be 82?

Problem 5 :

In Kevin's opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Kevin and he thinks that Kevin's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight is less than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Kevin?

Problem 6 :

Find the average of first 20 natural numbers which are divisible by 7.

Problem 7 :

The average of four consecutive even numbers is 27. Find the largest of these numbers.

Problem 8 :

There are two sections A and B of a class, consisting 36 and 44 students respectively. If the average weight of the section A is 40 kg and that of section B is 35 kg, find the average weight of the whole class.

Problem 9 :

In John's opinion, his weight is greater than 65 kg but less than 72 kg. His brother doesn't agree with John and he thinks that John's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of John?

Problem 10 :

A batsman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find the average score after 16th match.

Answers

1. Answer :

Given : Average of 3, 11, 7, 9, 5, 3, 8, 19, 17, 21, 14 and x is 12.

Multiply both sides by 12.

117 + x = 144

Subtract 117 from both sides.

x = 27

So, the number should be in the place of x is 27.

2. Answer :

Given : The average age of 30 kids is 9 years.

Multiply both sides by 30.

sum of the ages of 30 kids = 270

Given : If the teacher's age is included, the average age becomes 10 years:

Multiply both sides by 31.

270 + age of the teacher = 310

Subtract 270 from both sides.

age of the teacher = 40 years

3. Answer :

Given : The average 6 numbers is 8.

Multiply both sides by 6.

sum of 6 numbers = 48

Given : If the 7^th number is included, the average becomes 10.

Multiply both sides by 7.

48 + 7^th number = 70

Subtract 48 from both sides.

7^th number = 22

4. Answer :

Given : The average score of 9 tests is 80.

Multiply both sides by 9.

sum of the scores in 9 tests = 720

Let x be his score in his next test.

Given : Average score of 10 tests is 82.

Multiply both sides by 10.

sum of the scores in 10 tests = 820

sum of the scores in 9 tests + x = 820

720 + x = 820

Subtract 720 from both sides.

x = 100

So, David score in the next test should be 100.

5. Answer :

Let Kevin's weight be x kg.

According to Kevin, we have

65 < x < 72

According to Kevin's brother, we have

60 < x < 70

According to Kevin's mother, we have

x < 68

The values of x which satisfy all the above inequalities are 66 and 67.

So, the different probable weights of Kevin are 66 kg and 67 kg.

Average of 66 and 67 = ⁽⁶⁶ ⁺ ⁶⁷⁾⁄₂

= ¹³³⁄₂

= 66.5

So, the average of different probable weights of Kevin is 66.5 kg.

6. Answer :

The first natural number which is divisible by 7 is 7.

The next numbers which are divisible by 7 are 14, 21.....
Write the first twenty natural numbers which are divisible by 7.

They are 7, 14, 21, 28........ up to 20 terms.

Find the sum of all the above numbers.

= 7 + 14 + 21 + 28.........up to 20 term

Because all of the above numbers are divisible by 7, we can factor 7.

= 7(1 + 2 + 3 + 4 +.........+ 20)

= 7(210)

= 1470

Average of first 20 natural numbers which are divisible by 7 :

= 73.5

7. Answer :

Let x be the first even number.

Then the four consecutive even numbers are

x, x + 2, x + 4, x + 6

Given : Average of the four consecutive even numbers is 27.

x + 23 = 27

x = 24

Largest number :

= x + 6

= 24 + 6

= 30

8. Answer :

For section A, average weight is 40 kg.

Multiply both sides by 36.

sum of the weights of 36 students = 1440

For section B, average weight is 35 kg.

Multiply both sides by 44.

sum of the weights of 44 students = 1540

Total weight of 80 students (whole class) is

= 1440 + 1540

= 2980

Average weight of the whole class :

= 37.25 kg per student

9. Answer :

Let x be John's weight.

According to John, we have 65 < x < 72.

According to his brother, we have 60 < x < 70.

According to his mother, we have x ≤ 68.

The values of x which satisfy all the above three conditions are 66, 67 and 68.

Average of the above three values :

= 67

So, the average of different probable weights of John is 67 kg.

10. Answer :

Let x be the average after 16^th match. Then, the average after 17^th match is (x + 3).

Average after 17 matches = x + 3

Multiply both sides by 17.

total runs scored in 17 matches = 17x + 51 ----(1)

Average after 16 matches = x

total runs scored in 16 matches = 16x

Given : Runs cored in 17th match = 87.

total runs scored in 17 matches = 16x + 87 ----(2)

From (1) and (2),

17x + 51 = 16x + 87

x + 51 = 87

Subtract 51 from both sides.

x = 36

So, the average score after 16th match is 36.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.