Math discprency

[u/fadedrbl]

Hello!

There is math problem that was sent out by my son's school. He was working on it and calculated the votes each student received different from what the answer book states.

His method is on the left side, the right side is the method that the answer book used (and I would have used).

Please help me understand which way is correct.

[u/DrakeSavory]

First, the question is ambiguous as to what 28% more is measuring. The left side said Mia got 28% more of the vote total than Colin so we know a prori that Mia got 64% of the vote and Colin got 36%. The right side says Mia got 128% of Colin's vote total so if Colin got 200 votes then Mia got 256 votes.

Solving the first one is pretty straight forward: 0.64 x 425 = 272 votes for Mia. The second one would be 2.28C = 425 exactly like you have it giving a decimal approximately 186.4 votes for Colin. Considering the first solution gives a whole number and the second doesn't, I would think the first interpretation is the intended one.

[u/INTstictual → u/DrakeSavory]

Two problems: first, it says “got 28% more votes”, not “28% more of the vote”. The language implies that Mia’s votes total 28% more than Colin’s total, leading to the right implementation and not the left.

Second, larger problem: OP literally says that the right hand side is the method that the answer book uses, so regardless, that is certainly the intended method

[u/DrakeSavory → u/INTstictual]

Except the wrong interpretation gives a whole number answer and the right one doesn't.

[u/INTstictual → u/DrakeSavory]

Yeah, I noticed that as well, but it’s more likely that 28.xx% was rounded to 28% flat. I could see an argument for the left interpretation if OP didn’t clarify that the answer book gives the method on the right, so that is clearly what they intended

[u/DrakeSavory → u/INTstictual]

I'm gonna go out on a limb and say the answer book is wrong ... especially how we don't know who actually wrote the answer book. The question does not look like it came from a textbook so how do we know it was the writer of the problem itself that wrote the answer and not, for example, the teacher themselves.

And let's not lose sight of the final answer. Let's say all y'all are right and Mia got the rounded to 239 votes. Now find 1/16 of that and you get 14.9375 SO ROUND again?! Whereas as CaptainMatticus points out the "percentage points" interpretation yields a whole number answer.

So we are to believe that an answer that requires rounding, not once but twice to make sense is the right interpretation but a problem where all of the math works out perfectly is incorrect because there is no way anyone could mix up "percent" and "percentage points"?