Another algebra question

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

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.

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.

Oops, I'll edit my post. Thanks for finding the error.

Originally posted by twilight2007
Oops, I'll edit my post. Thanks for finding the error.

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

What Twilight2007 does can be done a bit faster using matrices. The method used by him/her is by far the most enlightening method 🙂

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 🙂