Question

If 9 is added to a number and the sum is multiple by 8 the result becomes 32 times the number. Find the number.​

Answer 1

• The number is 3.

Given :–

• If 9 added to a number and their sum is multiply by 8 then it becomes 32 times the number.

To Find :–

• The number.

Solution :–

Let,

The number be x.

According to the given condition,

If 9 added to a number.

$\longmapsto (9 + x)$

And their sum is multiply by 8.

$\longmapsto (9 + x) \times 8$

Then, it becomes 32 times the number.

$\longmapsto (9 + x) \times 8 = 32 \times x$ –––(1)

Now, solve this.

$\longmapsto (9 + x)8 = 32x$

Open the bracket.

$\longmapsto 72 + 8x = 32x$

$\longmapsto 8x - 32x = 72$

$\longmapsto -24x = 72$

$\longmapsto x = \cancel{\dfrac{-72}{-24}}$

$\longmapsto x = 3$

Check :–

Substitute the value of x in eqn. (1),

• x = 3

So,

$\longmapsto(9 + x) \times 8 = 32 \times x$

$\longmapsto(9 + 3) \times 8 = 32 \times 3$

$\longmapsto12 \times 8 = 96$

$\longmapsto 96 = 96$

Since, the L.H.S. and the R.H.S. are equal.

I.e.,

$\longmapsto 96 = 96$

So, the value of x = 3 is correct.

Answer 2

Given :-

If 9 is added to a number and the sum is multiplied by 8, the result becomes 32 times the number.

To find :-

The number.

Solution :-

Let the number be x.

★ If 9 is added to the number,

Then,

The number = (x+9)

★ The sum is multiplied by 8 , the result becomes 32 times the number.

According to the question,

8(x+9) = 32x

=> x+9 = $\sf \frac{32x}{8}$

=> x+9 = 4x

=> x-4x = -9

=> -3x = -9

=> x = $\sf \frac{-9}{-3}$

=> x = 3

Therefore, the number is 3.

_______________

Verification :-

Number = 3

If 9 is added to the number, the number becomes (3+9) = 12

According to the question,

8×12 = 32 × 3

→ 96 = 96

Hence Verified !