If 96 g of the mixture are prepared, what amount (in grams) of each chemical is needed?

Question

In a chemical mixture, 3 g of chemical A are used for each gram of chemical B, and 4 g of chemical C are needed for each gram of B. If 96 g of the mixture are prepared, what amount (in grams) of each chemical is needed?

chemical A 

chemical B 

chemical C

Answer 1

A = 3B

B = B

C = 4 B

3B + B + 4B = 96

8B = 96

B = 12

Answer 2

Hello, Alyssa,

There are several ways to solve this problem, including calculating a percentage of each component. I did the following. Ingredients A and C were both related directly to one B. I set the first column to the exact ratios provided, so that if we started with 1 gram of b and added the other two in the amount specified. That would make a sample of 8 grams. Since we want 96 grams, I multiplied each amount in the first column by 96/8, or 12 (right column). That provides the amounts of each to make a total of 96 grams.

Bob