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This is not a homework problem. This is a discussion between me and my Army buddies. One of my friends included a word problem in this post:

Ryan has a collection of $220$ baseball cards. He lets his brother have $1/4$ of his collection and sells $20\%$ of his collection to the baseball card shop. He takes $15$ cards to school to give his friends. How many baseball cards remain in Ryan’s collection?

Can someone give me an answer to this question? I’m in a heated debate. haha

Most of the answers given are $117$. My response was this:

  • Starting cards: $220$

  • "He lets his brother have 1/4 of his collection": $$\frac{220}{4}=55 \qquad\to\qquad 220-55= 165 \text{ cards} \tag{1}$$

  • "and sells 20% of his collection": This depends on exactly what is meant. As is written, because it says "and", I would take this to mean $20\%$ off the initial collection of $220$ cards, which I will call Situation A (or just "A" for short). In Situation B (or simply, "B"), I will take the $20\%$ off of the remaining $165$ cards. But grammatically, I believe this sentence to resemble Situation A.

    Situation A: $$220\cdot 0.2=44 \qquad\to\qquad 165-44=121 \tag{2a}$$ Situation B: $$165\cdot 0.2=33 \qquad\to\qquad 165-33=132 \tag{2b}$$

  • “He takes $15$ cards to school to give his friends”:

    Situation A: $$121-15=106 \tag{3a}$$ Situation B: $$132-15=117 \tag{3b}$$

So, as written, I believe your answer is $106$. If the Situation B was intended, your answer is $117$. Mathematically, I believe this problem would be written out as $$220-(220\cdot 0.25)-(220\cdot 0.20)-15=106$$

The reason I read this as I do is because when I read "He lets his brother have $\frac14$ of his collection and sells $20\%$ of his collection to the baseball card shop. He takes 15 cards...", I read "collection" as variable $A$, and $A=220$. So, when I see "collection" again, I inevitably see $A=220$.

One of the comments said the women were saying $106$ and the men $117$. I guess I'm a woman.

So, which answer is correct?

Thank you.

Blue
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Curious Layman
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  • Looking at the structure of the sentence, I'd say the women are correct – Righter May 17 '21 at 03:48
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    Situation A is more likely interpretation as for situation B, it should have said of remaining collection – Math Lover May 17 '21 at 03:50
  • If "I give half my collection to my daughter and half my collection to my son", did I keep 25% of the original collection? I say not; each child got 50%. So your A is what sounds right. – 2'5 9'2 May 17 '21 at 04:29
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    As suggested, it's an ambiguously-worded question, so contradictory interpretations are to be expected. I'll add another wrinkle, just for fun: The text says that Ryan "takes $15$ cards to school to give his friends", but it doesn't say that he actually succeeded in giving any of them away. (Intention is not action.) So the possible outcomes can be as high as $15$ more than listed. .. In any case, this is not really a math problem. Puzzling.SE would be a better place for this kind of question; maybe even English.SE. – Blue May 17 '21 at 04:31

1 Answers1

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Here is how the $117$ answer came about but it is wrong.

$$220/4=55\quad 220-55=165\quad 165\cdot20\%=33\quad 220-55-33-15=117$$ The reason this is incorrect is because the "problem" refers to his "collection" (meaning the whole collection, not what is left over) for both cases of $1/4$ and $20$% so they both refer to a fraction of $220$ and can "operate" in either order without changing the result.

poetasis
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