Question

if 9 is added to 4 times a number, it becomes the same as when 8 is subtracted from 5 times the same number. Find the number?​

Answer 1

Answer :-

• The required number is 17.

Given :-

• If 9 is added to 4 times a number, it becomes the same as when 8 is subtracted from 5 times the same number.

To find :-

• The number.

Step-by-step explanation :-

Detailed explanation of the solution :-

Let's understand!

• It has been given in the question that if 9 is added to 4 times a number, it becomes the same as when 8 is subtracted from 5 times the same number. We have to find the number.

• We will make an equation using the following statements and then find out the number after solving it.

Calculations :-

Let the number be x.

Then 4 times the number = 4x.

Now let's add 9 to the expression.

We get 4x + 9.

Now, the other number will be x too, since it's given in the question that the number is same as the other.

Then 5 times the number = 5x.

Now let's subtract 8 from the expression.

We get 5x - 8.

In the question, it's given that both the expressions are equal.

So, we are going to construct an equation now.

We have :-

$\sf4x + 9 = 5x - 8$

Transposing 9 from LHS to RHS, changing it's sign,

$\sf4x = 5x - 8 - 9$

Transposing 5x from LHS to RHS, changing it's sign,

$\sf4x - 5x = - 8 - 9$

On simplifying,

$\sf -x = - 17$

Removing the negative sign,

$\sf x = 17.$

The value of x = 17.

Thus, the required number is 17.