Question

When thirteen is reduced by two-thirds of a number, the result is 7. Find the number.

The number is

Answer 1

Given that :

• Thirteen is reduced by two-thirds of a number. And their result is 7.

To Find :

• The number.

Solution :

Let's assume the number as x

According to the question :

`\qquad \sf \: { \dashrightarrow (2)/(3)x - 13 = 7 }`

Adding 13 to both sides we get :

`\qquad \sf \: { \dashrightarrow (2)/(3)x - 13 + 13 = 7 + 13 }`

`\qquad \sf \: { \dashrightarrow (2)/(3)x = 20 }`

Now, Multiplying both sides by
`(3)/(2)` we get :

`\qquad \sf \: { \dashrightarrow (2)/(3)x * (3)/(2) = 20 * (3)/(2) }`

`\qquad \sf \: { \dashrightarrow ( \cancel2)/( \cancel3)x * \frac{{ \cancel3}}{ \cancel{2}} = \cancel{20} * \frac{3}{ \cancel{2}} }`

`\qquad \sf \: { \dashrightarrow x = 10 * {3} }`

`\qquad \bf \: { \dashrightarrow x = 30 }`

Therefore, The number is 30.

Answer 2

30

Explanation:

Let,

The req. number be = x

So,

Two - thirds of the number

`= (2)/(3) x`

Then, it is reduced by 13

`= (2)/(3) x - 13`

After that,

The req. result we get is = 7

Therefore,

By the problem,

`= > (2)/(3) x - 13 = 7`

• (On putting like terms on one side)

`= > (2)/(3) x = 7 + 13`

• (On Simplification)

`= > (2)/(3)x = 20`

• (On multiplying both sides with 3/2)

`= > (2)/(3) x * (3)/(2) = 20 * (3)/(2)`

• (On Simplification)

=> x = 30

Hence,

The req. number is 30.