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word problem

 
 
yitwail
 
Reply Tue 26 Jun, 2007 10:19 pm
i came across this problem in a substitute teacher training course. i'm fairly certain what the right answer is, but a surprising number of classmates thought differently. i would be obliged if you not only provide an answer, but also an explanation for your answer. here's the problem exactly as it's written:

A boy bought a bicycle for $50 and sold it to a neighbor for $60. He then bought the bicycle back for $70 and sold it again for $80. What do you think was the financial outcome of these transactions?
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Type: Discussion • Score: 0 • Views: 2,010 • Replies: 31
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cicerone imposter
 
  1  
Reply Tue 26 Jun, 2007 10:23 pm
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
0 Replies
 
yitwail
 
  1  
Reply Tue 26 Jun, 2007 10:56 pm
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!
0 Replies
 
Letty
 
  1  
Reply Wed 27 Jun, 2007 11:59 am
Math marking, M.D. Razz
0 Replies
 
neologist
 
  1  
Reply Wed 27 Jun, 2007 12:17 pm
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
0 Replies
 
Letty
 
  1  
Reply Wed 27 Jun, 2007 01:49 pm
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.
0 Replies
 
yitwail
 
  1  
Reply Wed 27 Jun, 2007 02:12 pm
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.

neologist wrote:
The fact that he bought the same bicycle back is irrelevant.


i think so too, but for those who reason differently, *why* is it irrelevant?
0 Replies
 
cicerone imposter
 
  1  
Reply Wed 27 Jun, 2007 02:16 pm
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.
0 Replies
 
Walter Hinteler
 
  1  
Reply Wed 27 Jun, 2007 02:25 pm
Right, and it has nothing to do if it was just one and same bike or two different.
0 Replies
 
fresco
 
  1  
Reply Wed 27 Jun, 2007 02:39 pm
Start with say $100 float...end up with $120. This allows you to teach the point without algebraic abstractions.
0 Replies
 
Eva
 
  1  
Reply Wed 27 Jun, 2007 03:21 pm
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! Laughing )

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?!
0 Replies
 
yitwail
 
  1  
Reply Wed 27 Jun, 2007 03:50 pm
if i knew, would i be asking a2k? $20 (probably) Razz

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


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


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* Shocked

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. Laughing
0 Replies
 
TTH
 
  1  
Reply Wed 27 Jun, 2007 03:58 pm
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.
0 Replies
 
fresco
 
  1  
Reply Wed 27 Jun, 2007 05:00 pm
Quote:
fresco wrote:
Start with say $100 float...end up with $120. This allows you to teach the point without algebraic abstractions.


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*



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")
0 Replies
 
spendius
 
  1  
Reply Wed 27 Jun, 2007 05:18 pm
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.
0 Replies
 
cicerone imposter
 
  1  
Reply Wed 27 Jun, 2007 05:20 pm
I see spendi had enough will power to pull himself away from his pub to post his nonsense.
0 Replies
 
spendius
 
  1  
Reply Wed 27 Jun, 2007 05:32 pm
Nonsense maybe but not stark staring bonkers like your solutions.
0 Replies
 
cicerone imposter
 
  1  
Reply Wed 27 Jun, 2007 05:35 pm
At least most of try to answer the question at the risk of being wrong.

You're wrong before even trying.
0 Replies
 
yitwail
 
  1  
Reply Wed 27 Jun, 2007 06:37 pm
fresco wrote:

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")


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?
0 Replies
 
Pauligirl
 
  1  
Reply Wed 27 Jun, 2007 06:54 pm
yitwail wrote:
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.

neologist wrote:
The fact that he bought the same bicycle back is irrelevant.


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


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
0 Replies
 
 

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