I don't mean to waste your time with this simple thing but I came here because I haven't found a solution. The textbook is Mathematics All Around 5th ed. by Thomas Pirnot. The exercise says:
"Assume the board of trustees for your school is bound by state law to increase tuition by no more than 10% over the next three years. If tuition is raised by 2%, then 3%, and then 5%, has the board followed its mandate?"
So I figured from a previous related exercise that incrementing tuition by, say, 2% and then 3% is not the same as increasing it by 3% and then 2%.
So this is how I rephrased the question assuming that tuition is 1: Is 1.1 $\geq$ 1.05 (1.03 (1.02))?
No, because 1.1 $\lt$ 1.10313. So the board hasn't followed its mandate.
I think the way I calculated the increase is wrong because if incrementing by 2%, then 3% and finally 5% was calculated with plain multiplication then it doesn't matter in which order I multiply the 1.02, 1.03 and 1.05. But it does matter. What am I doing wrong here?
Update: I think I figured it out. I should have taken into account the "over 3 years" part. Assuming that each increase corresponds to years 1, 2 and 3:
Is 1.02 + 1.03(1.02) + 1.05(1.03(1.02)) $\leq$ 1.1 $\times$ 3?
The answer is yes, 3.17373 $\leq$ 3.3, so the board has followed its mandate. The related exercise that I mentioned was:
"The board of trustees is considering a tuition increase. Some want to raise it by 5% this year and 8% the next. Some want to raise it by 8% this year and 5% the next. Some say that it doesn't matter because you will end up paying the same. Does it make any difference?"
Assuming that tuition is 1, then 1.05 + 1.08(1.05) $\neq$ 1.08 + 1.05(1.08). So the order does matter when the increases have to be added like in this case.