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

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Answer 1 · 2017-10-14T16:02:09

See 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.