Why am I getting two different answers?

Question

If I add 45% to $4.46 and get $6.46 why do I get $6.55 when I add 40% and then 5% to the same $4.46?

Which one is correct?

The $4.46 is the original price, the 40% is a profit margin and the 5% is sales tax.

Answer 1

When you add 45% to a number x, you increase it to 1.45x.

If you add 40% to x, it increases to 1.40x. If you add an extra 5% AFTER you already added 40%, it creases to

1.05(1.40x) = 1.47x

Note that 1.47x > 1.45x

The reason the results are different is that in one case you do a simple increase of 45% while in the other you do a compounded increase of 5% on top of the 40% increase. The way the question is worded, I would say you should add the 5% after the price was increased by 40%, which results in the higher number.