How many of $220$ baseball cards are left after giving away $1/4$ of them, selling $20\%$, and giving away another $15$?

Question

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.

Answer 1

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.