Question

Marcus says "If you increase a number by 20% and then you take the answer and decrease it by 20% you don't get back to the number you started with." Is Marcus correct? Explain how you know

Answer 1

See explanation.

Explanation:

If the initiol number is `x` then the steps can be described as follows:

I step

Increasing by `20%`: the number becomes

`x+20%x=x+0.2x=1.2x`

II step

Decreasing the new number by `20%`:

`1.2x-20%*1.2x=1.2x-0.2*1.2x=1.2x-0.24x=0.96x`

The final number is `0.96x`, so it is less than the original number `x`.

This explanation proves that the statement is correct.