Question

One fifth of a number added to half of it is equal to 9 less than the number find the number

Answer 1

Let, the number be 'X'

∴1/2 of X = X × 1/2 =X/2

∴1/5 of X = X × 1/5 = X/5

By condition,

(X/5) + (X/2) = X -9

⇒(2 X + 5 X) ÷ 10 = X - 9

⇒ 7 X = 10 × ( X -9)

⇒ 7 X = 10 X - 90

⇒ 7 X + 90 = 10 X

⇒ 90 = 10 X - 7 X

⇒ 90 = 3 X

⇒ 3 X = 90

⇒ X = 90 ÷ 3

⇒ X = 30

∴ The number is 30

Answer 2

Concept:

Mathematical equation is a relation between two or more mathematical quantities, numbers, mathematical variables etc. by equal sign.

Given:

Given that, one fifth of a number added to half of it is equal to 9 less than the number.

Find:

We have to find the initial number.  

Solution:

Let the initial number be = x

One fifth of a number = x/5

One fifth of a number added to half of it =x/5 + x/2

According to the question, the above value is 9 less than the number.

So the suitable mathematical equation is,

x/5 + x/2 = x - 9

(5x+2x)/10 = x-9, LCM of 5,2 = 10

7x/10 = x-9

7x = 10x - 90

10x - 7x = 90

3x = 90

x = 90/3

x = 30

Hence the initial number is 30.

#SPJ2