Question

Dennis thinks 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 the number Dennis thinked of be x. Then after adding 0.5 to that number his new number will be x+0.5. Multiplying that new number by 4 will get him $4(x+0.5)=4x+2$. Subtracting 2 from that will yield him 4x. Finally, dividing that number by two he gets 2x as his final number.

From this we get that 2x=48, from which x=24, the original number.

We can check this result. Adding 0.5 to 24 will get you 24.5. Multiply that by 4 and you get 98. Subtract 2 from 98 and it's 96. Finally, divide it by 2 and your final answer will be 48. So indeed, Dennis started with the number 24.