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A certain adhesive is formed by mixing 2 components, a resin and a hardener, and allowing the mixture to dry. For example, 2 grams of resin mixed with 2 grams of hardener will result in 4 grams of adhesive. A worker has 6 grams of resin and 8 grams of hardener and wishes to form adhesive using one of the following mixture formulas:
Select for Mixture A the maximum amount, in grams, that the worker can make of Mixture A, and select for Mixture B the maximum amount, in grams, the worker can make of Mixture B, according to the information provided. Make only two selections, one in each column.
5
6
10
12
14
Let's create a table to organize our information:
| Component | Available | Mixture A Ratio | Mixture B Ratio |
|---|---|---|---|
| Resin | 6 grams | 3 parts | 2 parts (or 1) |
| Hardener | 8 grams | 2 parts | 4 parts (or 2) |
| Total Parts | 5 parts | 6 parts (or 3) |
Key insight: Mixture B's ratio 2:4 simplifies to 1:2 for easier calculation.
We need to find the maximum amount of each mixture we can make given our limited resources. The limiting factor will be whichever component runs out first.
For Mixture A (3:2 ratio):
For Mixture B (1:2 ratio):
Let's check which component limits us:
Since we only have 6g resin (not 12g), resin is our limiting factor.
Maximum Mixture A:
Let's check which component limits us:
Since we only have 8g hardener (not 12g), hardener is our limiting factor.
Maximum Mixture B:
Final Answer:
We've efficiently used our limited resources to maximize each mixture type, with resin limiting Mixture A production and hardener limiting Mixture B production.