The document describes finding the ratios of products A, B, and C using a closed model system of equations. It provides the equations that model the proportions of the three products as variables X1, X2 and X3, which sum to 1. Solving this system of equations will reveal the values of each variable and the ratio of A:B:C in lowest terms.

1. Find the ratios of products A, B, and C using a closed model. The ratio A: B : C is (Type your
answer in lowest terms, using an integer for each number.)
Solution
consider the proportions three products A,B,C as Xi =1,2,3...
The product model is as follows:
0.3X1 +0.2X2 +0.1X3 =X1
0.2X1 +0.6X2 +0.1X3 =X2
0.5X1 +0.2X2 +0.8X3 =X3
X1 +X2 +X3 =1
Solve the above equaltions to get the values of X1, X2 , X3 and ratio of the proportions