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Who's right?

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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/09/2015 at 23:26
jonoMT View Drop Down
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Problem from our son's math book:


My wife and I both looked at it with him independently and came up with the same answer: $13.35
But he came home today and said the teacher's book says $26.70. I don't see how that can be unless the friend spent 2/3 of her money on lunch.

I worked it out this way:
2/3m + 2.50 (loan repayment) - 4.00 - 2.50 = 4.90
2/3m - 4.00 - 2.50 = 4.90 - 2.50 = 2.40 (cancelling out the loan repayment)
2/3m = 2.40 + 4.00 + 2.50 = 8.90
8.90 / 2 = 4.45
4.45 * 3 = 13.35 = m

If we're both mathematic idiots, then we welcome being corrected. Otherwise, I'm going to make two points to my son:

1) Trust your own work
2) Don't always believe that someone is right because they are an authority
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 03:35
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Having taught a lot of college classes and professional seminars, my guess is that somebody changed the problem without changing the answer!  I've seen that happen a number of times.  Either that, or the textbook author majored in something like transgender studies!




Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 04:26
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Now that's funny!!!
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 05:38
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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 05:39
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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 07:06
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Call Ted, he'll know! Big Grin
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 13:02
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I came up with $15.16, because the $2.50 for the loan should not have been included in the final figureBucky
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 13:16
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If the problem above is stated correctly, the answer is $13.35.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 13:40
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Thanks.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 13:54
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So how many other kids in class came up with $26.70?
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 16:28
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I worked the problem out to be $26.70.  Here's how:

FIRST, subtract the $2.50 from the $4.90 that the friend has left, leaving you with the remainder of the money owned BEFORE lunch (that's the key--she didn't have the 2.50 before lunch).  Then the problem looks like this:

1/3(x) - 4.00 - 2.50 = 2.40; (2.40 = 4.90 - 2.50 (received after lunch)).  Solve for x;
X = 3(2.40 + 2.50 + 4.00)
X = 3(8.90)
X = 26.70


Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 16:40
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I got a hernia just reading that.

I deal in percentages, margin ,
markup and commissions.

That's it!

😎
,
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 16:46
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...and the correct answer is $13.35.  My problem above just shows how folks can improperly set up the problem to arrive at the wrong answer.  Who can see how I incorrectly set up the problem?
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 17:14
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Originally posted by DCAMM94 DCAMM94 wrote:

...and the correct answer is $13.35.  My problem above just shows how folks can improperly set up the problem to arrive at the wrong answer.  Who can see how I incorrectly set up the problem?

You set the problem up with erroneous initial constant. 
 There is a simpler way to do this, but this way shows most of the work.  There are also more complex methods that show ALL the tedious work.  

X-1/3X = 2/3X

2/3X+2.50 -6.50 = 4.90 ( could go directly from here to 2/3X = 8.90)
2/3X+2.50 = 4.90+6.50 = 11.40
2/3X = 11.40-2.50= 8.90
3/2 * 2/3X = 8.90 * 3/2 (or X = 8.90/2 *3 = 4.45 * 3 = 13.35)
X = 26.70/2 = 13.35
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 17:22
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Just got another hernia, thanks for the double guys!

😎😎
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 17:30
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Absolutely correct, though I set up and worked the problem a little differently.  Jono's kid was right - the teacher solved the problem incorrectly.  CALL THE SCHOOL BOARD!!!!
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 17:54
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Fire those bastards!!!

No tenure!!! I don't get it why should they?
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 18:16
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Jono… tell your son… First, he is correct, second, always check and double check your work… make sure you are right… then NEVER, NEVER, NEVER quit (or give up your correctness).  
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 19:06
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I agree as well, the correct answer is 13.35. The book was probably written using common core math.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 19:38
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The answer is indeed $13.35, but you boys are making it waaaaaay more complicated than it is.

As stated above, she was given the $2.50 AFTER lunch, which means it wasn't a part of her original $ tally at lunchtime. The fact it was canceled out by her spending that exact amount on snacks is therefore irrelevant, and it should be totally ignored and omitted from the problem. That was put there as diversion to try to trip you up.

She spent $4 of her original money after lunch, leaving $4.90. This means she had $8.90 of her original money remaining after she bought lunch. Again, totally ignore the $2.50, as it's irrelevant since she didn't have it at lunchtime. 
$8.90 is 2/3rds (or 67%) of her original $ total.

The math:

2/3 = 0.6666667 (An infinite decimal number that you can't round up less than 3 decimal places or you'll get incorrect answer).

(X*0.6666667)=8.90

X=8.90/0.6666667
=$13.35
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/10/2015 at 19:45
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S**t, now I have a triple hernia!

Way to go brother.

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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/11/2015 at 06:27
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I screwed up at the end cause I rushed and ddi it in my head....
 
 
I immediately saw that the $2.50 should be ignored.  I boobooed when I said $8.90 was  one third not 2 thirds of the total... So I came up with books answer of $26.70.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/11/2015 at 07:27
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Originally posted by DCAMM94 DCAMM94 wrote:

...and the correct answer is $13.35.  My problem above just shows how folks can improperly set up the problem to arrive at the wrong answer.  Who can see how I incorrectly set up the problem?

This^^^^^^^

My math:


Ignore the $2.50.  Divide $8.90 by 2 and multiply the answer by 3  $8.90/2=$4.45  $4.45*3=$13.35

Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/11/2015 at 11:57
jonoMT View Drop Down
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IMO, the problem and the type of thinking it's meant to encourage would have been made clearer if they had chose a value other than $2.50 for the loan repayment. Making it the same as another amount in the equation (the snack purchase) made it harder to explain to my son. If, for example, it had been $3.00 then it would be easier to make the point.

That could have led to a demonstration with a Quickbooks ledger or a P&L statement...just ways to show him that this stuff matters in the business world.

While it wasn't the teacher's mistake initially, she also didn't choose to verify the correct answer. While I won't make a big deal about it, I will talk to her. Like I initially mentioned it's important that he learns to trust our judgment and not blindly accept answers just because"that's what the book says."
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: September/11/2015 at 12:00
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Excellent
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