I'm confused on how you can approach this problem using Gauss-Jordan elimination.
I’m buying three chemicals, call them A, B and C. One kg (kilogram) of A takes up 100 cc (cubic centimeters) and costs $50.
One kg of B takes up 200 cc and costs $40.
One kg of C takes up 500 cc and costs $30.
I bought 30 kg of chemicals, taking up 7500 cc, and costing $1210.
How much of each chemical did I buy?
Can anyone explain this to me? Much appreciated!
On
Let $A,B,C$ be the quantities of the tree chemicals that you buy, so you have a first equation: $$ A+B+C= 30 $$ The volume of the three is: $$ 100A+200B+500C = 7500 $$ and the cost is: $$ 50A+40B+30C=1210 $$ so you have a system with three linear equation that can be solved with Gauss-Jordan elimination.
When dealing with problems where you don't know where to start from, it's a good idea to reduce the problem to something you know. Case in point, in this problem, start from the last line, how much of each chemical did you buy? Assume you bought $x$ kg of A, $y$ kg of B and $z$ kg of C. Next thing you know, the total weight of all the chemicals you bought is 30 kg. Can you express it in terms of $x$, $y$ and $z$? Yes, you can. $$x+y+z=30$$ Next piece of information is the volume of the chemicals you bought. You know how much volume each chemical takes up. From that, you get $$100x+200y+500z=7500$$ And finally, you know how much money you spent on each chemical $$50x + 40y+30z=1210$$ So, now you have 3 linear equations in 3 unknowns. You can use gaussian elimination to solve for $x$, $y$ and $z$ now.