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Help needed to solve math problem


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Hi Sterling!

If you have 3 variables but only 2 equations there isn't one and only solution. The way to solve it properly is:

You can fix a variable (egg a= a number) and the solve the other others. you'll find 2 variables depending on the one you fixed (egg b=3*a and c=8*a-5 just an example).

consedering the 2 lines you've written that would be:

a+b+c=100 (line1)

10a+3b+0.5c=100 (line2)

=> multiplying each side of the first line by 10:

10a+10b+10c=1000 (line1*10) let's call it line3

10a+3b+0.5c=100 (line2)

=>we can keep the first line and change the second into the substraction of the 2 lines

10a+10b+10c=1000 (line3)

7b+9.5c=900 (line3-line2) let's call it line4

now we can't go further as we had 2 lines for 3 variables.

but we can already solve in fact! Let's say c is any number. consider line4:

7b=900-9.5c => b=(900-9.5c)/7

now we've got c and b. We can go back to line 1 to find a:

a = 100 - b - c

a = 100 - (900-9.5c)/7 - c

a = 100 - (900-9.5c)/7 - (7c)/7

a = 100 - (900-9.5c-7c)/7

a = 100 - (900-16.5c)/7

and we have all the solutions (including negative ones): smart



a = 100 - (900-16.5c)/7

Bu as we only want integers from 0 to 100 in this problem you can try for each integer c from 0 to 100 to find a and b and see if there are integers also. Excel does it quickly:

http://www.membres.lycos.fr/yoyorex/xls/iceCreamProblem.xls (right-click and download, solutions are in red)

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Sterling...Nope, I'm a 39 year old mom homeschooling my 13 and 16 year old children. I think part of the problem is that I really stunk at math in school.

I think for one thing, I had one of the worst text books I could've gotten, but the good news is....my 16 year old took his end of geometry exam...made an 80, so at least I know he learned something.

Anne, that's not a bad idea. I'll take any advice I can get too. The steps for the proofs are so long and drawn out. Thank heavens tomorrow is our last day. I can regroup this summer and buy books I'm confident in.....any suggestions Sterling? I kinda liked the Saxon book I used last year. Any advice will be welcome!


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Although geometry was my least favorite math subject, I found long proofs beautiful --as long as it really took that many steps to get there. What drove me batty was those who did in 15 steps what could be done more efficiently in 5. Hence, the 'game'.

If a particular subject frustates you, find a new way to approach it. A different look often helps make it more tolerable.


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