The greatest amount of brass Fred can make is 4 kg.
The Breakdown
According to the given information, the ratio of copper to zinc in brass is 7:3. This means that for every 7 parts of copper, we need 3 parts of zinc.
For every 7 kg of copper, we need 3 kg of zinc. So, we can calculate the maximum amount of brass Fred can make by dividing the amount of copper and zinc by their respective ratios:
Maximum amount of brass = min(35 kg / 7 kg, 12 kg / 3 kg)
Calculating this, we find:
Maximum amount of brass = min(5, 4) = 4 kg
Therefore, the greatest amount of brass Fred can make is 4 kg.