Hi All,
This question is essentially just a wordy weighted average question.
We're given the composition of 2 types of alloy bar:
Bar A: 2 parts gold, 3 parts silver = 2/5 gold = 40% gold
Bar B: 3 parts gold, 7 parts silver = 3/10 gold = 30% gold
We're going to "mix" these two bar "types" and end up with a mixture that is 5/16 gold
We know that the total mixture will be 8kg. We're asked how many of the kg are Bar A.
A = # of kg of Bar A
B = # of kg of Bar B
Now we can set up the weighted average formula:
(.4A + .3B) / (A + B) = 5/16
And cross-multiply and simplify....
6.4A + 4.8B = 5A + 5B
1.4A = 0.2B
Multiply by 5 to get rid of the decimals...
7A = B
A/B = 1/7
This tells us that the ratio of A to B is 1:7. Since the total weight is 8kg, we must have 1 kg of Bar A and 7 kg of Bar B.
Final Answer:
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