# Another algebra question

joe shmo
Posers and Puzzles 31 Oct '07 22:31
1. joe shmo
Strange Egg
31 Oct '07 22:31
The chemical equation C3H8 +O2 = CO2 +H2O is not balanced

I know what coefficients are needed. Im Interested in the math to find them.

Baisically im looking for something to this effect

x(C3 + H8) + y(O2) = a(C + O2) + b(H2 + O )

Just using brainpower and guess and checking is obviously eisier, but im curious what the mathamatics would look like.

I set it up the way I did because it looked the most promising

I asked my algebra prof. she said something about matrices for a possible solution
2. 01 Nov '07 01:243 edits
Matrices aren't necessary. Also, guess and check is still easier. Here's to algebra:

Basically, you have 4 variables and several equations, namely:
3x=a
8x=2b
2y=2a+b

We only need to find the "smallest" set of a,b,x, and y, which makes this question possible. Otherwise, we would need 4 equations.

Using the first two equations, we can form a relation between a and b:
24x=8a
24x=6b
0=8a-6b
8a=6b
4a=3b

The smallest integer solution is a=3 and b=4. That means x=1. Now we solve for y.
2y=2a+b
2y=6+4
2y=10
y=5.

In conclusion, a=3, b=4, x=1, and y=5. Note this is possible only because we took the smallest integer solution for 4a=3b. Otherwise, at best, we would have the coefficients in terms of one variable.

Thanks to Joe Shmo for pointing out an error.
3. joe shmo
Strange Egg
01 Nov '07 01:58
Originally posted by twilight2007
Matrices aren't necessary. Also, guess and check is still easier. Here's to algebra:

Basically, you have 4 variables and several equations, namely:
3x=a
8x=4b
2y=2a+b

We only need to find the "smallest" set of a,b,x, and y, which makes this question possible. Otherwise, we would need 4 equations.

Using the first two equations, we can form a ...[text shortened]... tion for 2a=3b. Otherwise, at best, we would have the coefficients in terms of one variable.
First I thank you for showing me, I had an inkling of an idea, but not enough education.

only the answers you provided don't balance the equation.

On your second equation down If I have got the logic correct you have

8x=4b and believe it should be 8x=2b

could that be where your mistake is, I would check it myself but I'm not sure how exactly to solve this yet.
4. 01 Nov '07 02:01
Oops, I'll edit my post. Thanks for finding the error.
5. joe shmo
Strange Egg
01 Nov '07 02:09
Originally posted by twilight2007
Oops, I'll edit my post. Thanks for finding the error.
no,...... thank you twilight for helping out........now I just have to figure out how to do every thing else....haha

thanks, Eric
6. wolfgang59
Mr. Wolf
01 Nov '07 18:49
I'd basically do the same as Twilight only I would set x=1 right away and solve for 3 variables with 3 equations.

If you get non-integer solutions just multiply up.

In other words

(Carbon) ...... 3 = a
(Hydrogen) ... 8 = 2b
(Oxygen) ......2y = 2a + 2b
7. TheMaster37
Kupikupopo!
02 Nov '07 07:06
What Twilight2007 does can be done a bit faster using matrices. The method used by him/her is by far the most enlightening method ðŸ™‚
8. joe shmo
Strange Egg
02 Nov '07 12:09
Originally posted by TheMaster37
What Twilight2007 does can be done a bit faster using matrices. The method used by him/her is by far the most enlightening method ðŸ™‚
Whats cool about it, is that i can actually reproduce the results.....thanks in no small part to those here at RHP

I just had a hunch, but boy is it sweet when they turn out to be correct ðŸ˜€