word problem

Gained $80?

1. purchase for $50
2. Sold for $60 +$10 profit
3. purchase for $70 - $10 loss
At this point, he's even
4. He sold it for $80 $80 profit.

or he paid $50 + $70 = $120
he received $60 + $80 = $140
net cash gained $20

agree with you, ci; i think it's either $80, which would be other, or $20, but it's for you to decide which, not me. :wink:

anyone else, don't be deterred by my opinion or CI's; i want to know *your* opinion!

Math marking, M.D.

The fact that he bought the same bicycle back is irrelevant. He bought a bicycle for $50 and sold it for $60. Profit $10. He bought a bicycle for $70 and sold it for $80. Profit $10.

Gross profit = 2 X $10 = $20

First of all, I made the assumption that the boy had only $50.00, and then it would seem to me that if he didn't recoup his initial investment, which he didn't, he would have made zero profit.

i've also heard this reasoning: by selling for 60, he makes a $10 profit, but when he buys it again for 70, he loses 10 to break even, and then he makes $10 again by selling for 80, hence he comes out $10 ahead.



i think so too, but for those who reason differently, *why* is it irrelevant?

No matter how one interprets the words, he spent a total of $120, and received $140, his net gain is $20; it's not $10.

Right, and it has nothing to do if it was just one and same bike or two different.

Start with say $100 float...end up with $120. This allows you to teach the point without algebraic abstractions.

Letty sent SonofEva this problem on Sunday night, except in her version the question at the end read, "What do you think is his total profit."

The three of us argued about this for two straight days, figuring out different reasoning that would account for all four answers: $0, $10, $20 and $30. ($80's a new one! Wait'll I tell them! )

Finally, Hubby and I settled on the same answer -- $20.
My reasoning was the same as c.i.'s: "...he spent a total of $120, and received $140, his net gain is $20..."
Hubby's reasoning was the same as neologist's: "The fact that he bought the same bicycle back is irrelevant. He bought a bicycle for $50 and sold it for $60. Profit $10. He bought a bicycle for $70 and sold it for $80. Profit $10. Gross profit = 2 X $10 = $20"
(Remember, our version of the problem simply asked for the total profit.)

SonofEva couldn't decide between $20 and $10.
He said it is $20 if you count profit only. (Reasoning: 2 x $10 = $20, same as above)
But it is $10 if you count profit AND loss. (Reasoning same as yitwail's: "... by selling for 60, he makes a $10 profit, but when he buys it again for 70, he loses 10 to break even, and then he makes $10 again by selling for 80, hence he comes out $10 ahead."

So now we're dying to know, yitwail...WHAT IS THE CORRECT ANSWER?!

if i knew, would i be asking a2k? $20 (probably)

incidentally, letty didn't paraphrase the question. when i emailed her, i didn't have the exact wording so i sent her a paraphrase.




i've tried that approach, also, but the objection can been raised, "it doesn't say that in the problem," as well as accusations of posing a *trick question*

btw, since no one has come up with $30, here's a simple way. the boy starts with $50, and ends up with $80. ergo, he made $30.

The original post said "financial outcome". What defines financial outcome? Profit can be a definition. There are different definitions to "profit".
I think it is an unfair question imo.

Okay ....so I'll spell it out.

You let the class of students pick any float they like over $70. You then go round the class and they find they all announce they get $20 profit. So you ask "does that prove the answer ?" The brightest ones might say say "no" which is your cue as a teacher to introduce the algebraic float $X.

Whence X-50+60-70+80 = X+ 20.

The ultimate pedagogical point is the "utility of algebra" not "the answer" with respect to some forms of question.(as implied by the title "word problem")

Nah-

He wasted $50 on a contraption when he could have got one of the girls who advertise in Personal Services round, maybe two, for that amount and not had to think about his neighbours who are self-evidently stupid on the evidence of the facts as reported which I don't believe for one moment anyway.

I see spendi had enough will power to pull himself away from his pub to post his nonsense.

Nonsense maybe but not stark staring bonkers like your solutions.

At least most of try to answer the question at the risk of being wrong.

You're wrong before even trying.

but what if the problem is presented not to an algebra class, but a heterogeneous (wrt math knowledge) group of learners? can we justify the solution without introducing the unknown x?

Seems to me: Gross gain was $20.00 Net gain (after expenses) was $10.00. That's the financial outcome. Doesn't matter if it was the same bicycle or not.

That's also just my opinion.

P