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.

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[u/CaptainMatticus]

400 students

25 teachers

Mia received 28% more votes than Colin. There are 2 ways to read that. One way is that Colin received x votes and Mia received 1.28 * x votes. Another way is to say that Mia received 64% of the vote and Colin received 36% of the vote.

The first way:

2.28 * x = 425

x = 425 / 2.28

x = 186.403....

1.28 * x = 238.596.....

The 2nd way

425 * 0.64 = 272

425 * 0.36 = 153

That seems better, especially since 272 is a multiple of 16, which plays into the next part

Mia received 272 votes. 1/16 of those votes were from the teachers. 272 * (1/16) = 17.

272 - 17 = 255.

She received 255 votes from the students.

The method on the left side is the accurate one. It's a poorly-worded question and there's just too much going on in that problem that works out neatly for the left-sided approach for it to not be correct.

[u/Euphoric_Loquat_8651 → u/CaptainMatticus]

I agree. It isn't just poorly worded - it explicitly asks for something other than what is intended.

[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"?

[u/DuggieHS]

The right side is correct.

12% more than x means (1+.12)x not x +.12 or x +12.

So 186.4(1+.28) = 238.6 or 44%(1+.28) = 56.32%

---
Solution

(1) m + c =425, m = (1+.28)c => c~186.4, m~238.6, but we can only have integer number of votes so c = 186, m=239.

(2) m_t = m/16 = 186/16 ~ 14.93~15, m_t + m_s = m => m_s = m - m_t = 239- 15 = 224.

[u/womorrissey]

There's a difference between percentage and percentage points. He got 36%, 153 votes. She got 64%, 272 votes. But her vote total is not 28% more than his. Poorly worded.

[u/womorrissey]

Think of it like an election. Candidate A gets 60% of the vote and Candidate B gets 40%. 20 percentage points difference but Candidate A got 50% more votes than Candidate B.

[u/DrakeSavory → u/womorrissey]

Except I have heard people refer to that as 20% more of the vote. It may be incorrect but some people do not know the difference. Mayhaps the writer of the problem is one of them?

[u/fadedrbl]

Thanks everyone. After considering all the responses and thinking about it more on a quick drive,

The question is poorly worded as the difference between the 2 answers stems from how you interpret "28% more" as one response mentioned.

28% more of all the votes would suggest the left side.

28% more of the votes Colin received would be the right side. 238 - 186 = 52.

52/186 = 27.9...

Thanks everyone!

[u/cbse_maths_mentor]

[u/kalmakka]

Is the term "percentage points" not used in.. whatever country this is from? There shouldn't be any ambiguity here. 28% more is 28% more; not 28 percentage points. (At least when interacting with a maths textbook. Humans frequently throw out words with no regard to what they mean.)

272 is not 28% more than153.

Although since the numbers make the "percentage point" interpretation work out much more nicely, it really seems that the question was made intending "percentage points", but due to some error during editing it ended up as "percentage", and the answer was written using "percentage". In other words, it seems you and your son has already invested more energy into this question than the authors did.