Question

Harry thought of a number and doubled it. He subtracted 3 from the result and then multiplied it by 3 to get 105. What was the original number that Harry thought?

Answer 1

⇒ Given:

Harry thought of a number and doubled it.

He subtracted 3 from the result and then multiplied it by 3 to get 105.

⇒ To Find:

The original number Harry thought.

⇒ What should be done?

We will have to reconstruct the steps as given assuming the unknown number as any variable.

⇒ Solution:

Let the unknown number Harry thought be x.

Statement 1: It is given that he doubled the number and subtracted 3 from the result.

Forming an expression:

2x - 3

Statement 2: Harry then multiplied 3 to the result to get 105.

Forming an equation:

(2x - 3) x 3 = 105

→ Now, we can solve the equation:

$\sf{=(2x-3)\times3=105}$

→ Opening the brackets:

$\sf{=(3\times2x)-(3\times3)=105}$

→ Multiplying the terms:

$\sf{=6x-9=105}$

→ Moving the constants to the RHS:

$\sf{=6x=105+9}$

$\sf{=6x=114}$

→ Moving the constant multiplied to the variable to the RHS:

$\sf{=x=\dfrac{114}{6}}$

$\sf{x=19}$

Therefore Harry thought of the number 19.

⇒ Verification:

LHS:

(2x - 3) x 3 where x = 19.

= (2 x 19 - 3) x 3

= (38 - 3) x 3

= 35 x 3

= 105

RHS:

105

LHS = RHS

Hence verified!