**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 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 ?

**Solution : **

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

That is,

Sum of all the given numbers / number of numbers = 12

(3 + 11 + 7 + 9 + 5 + 3 + 8 + 19 + 17 + 21 + 14 + x) / 12 = 12

(117 + x) / 12 = 12

Multiply both sides by 12.

(117 + x) = 12 ⋅ 12

117 + x = 144

Subtract 117 from both sides.

x = 27

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

**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.

**Solution : **

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

That is,

Total age of 30 kids / 30 = 9

Multiply both sides by 30.

Total age of 30 kids = 9 ⋅ 30

Total age of 30 kids = 270

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

That is,

(Total age of 30 kids + Age of the teacher) / 31 = 10

(270 + Age of the teacher) / 31 = 10

Multiply both sides by 31.

270 + Age of the teacher = 10 ⋅ 31

270 + Age of the teacher = 310

Subtract 270 from both sides.

Age of the teacher = 40 years

**Problem 3 :**

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

**Solution : **

**Given : **The average 6 numbers is 8.

That is,

Sum of 6 numbers / 6 = 8

Multiply both sides by 6.

Sum of 6 numbers = 8 ⋅ 6

Sum of 6 numbers = 48

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

That is,

(Sum of 6 numbers + 7^{th} number) / 7 = 10

(48 + 7^{th} number) / 7 = 10

Multiply both sides by 7.

48 + 7^{th} number = 10 ⋅ 7

48 + 7^{th} number = 70

Subtract 48 from both sides.

7^{th} number = 22

**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 ?

**Solution : **

**Given : **The average score of 9 tests is 80.

That is,

Sum of scores in 9 tests / 9 = 80

Multiply both sides by 9.

Sum of scores in 9 tests = 80 ⋅ 9

Sum of scores in 9 tests = 720

Let "x" be his score in his next test.

**Given :** Average score of 10 tests is 82.

Then, we have,

(Sum of scores in 9 tests + x) / 10 = 82

(720 + x) / 10 = 82

Multiply both sides by 10.

720 + x = 82 ⋅ 10

720 + x = 820

Subtract 720 from both sides.

x = 100

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

**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 ?

**Solution : **

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

Average of 66 and 67 = 133 / 2

Average of 66 and 67 = 66.5

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

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**