Question

Dennis thought of a number. He adds 0.5 to that number and then multiplies the new result by 4. He then subtracts 2 and divides the number by 2. His final answer is 48. What number did Dennis start with?

Answer 1

Let Dennis thought x.

A/Q,

He adds 0.5 = x + 0.5

Then multiplies by 4 = ( x + 0.5 )4 = 4x + 2

Then he subtracts 2 = ( 4x + 2 - 2 ) = 4x.

Then he divides it by 2 = 4x/2 = 2x

He got 48 = 2x

⇒ 2x = 48

⇒ x = 48 ÷ 2

∴ x = 24.

So, Dennis had thought 24.

Answer 2

Given:

• Dennis thought of a number.
• Adds 0.5
• Multiplies by 4
• Subtracts 2 from it
• Divides by 2
• Result = 48

Solution:

Consider the number to be x.

1. Dennis adds 0.5. So, (x + 0.5)
2. Multiplies by 4. So, ( x + 0.5 )4. We get, (4x + 2)
3. Dennis subtracts 2. So, ( 4x + 2 - 2 ). We get, 4x
4. Divides by 2. So, 4x/2. We get, (2x)

He got the result as 48.

So, 2x = 48

Then,

x = 48 ÷ 2

x = 24

Hence, The number is 24.