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Difficulty: Very hardRatios, Rates, and Proportions

An industrial laboratory prepares a batch of Alloy ZZ weighing 260260 pounds, which consists solely of copper and zinc in a ratio of 7:67 : 6 by weight. A technician then adds 4040 pounds of pure copper to this batch to create Alloy WW. What is the ratio of copper to zinc in Alloy WW?

  1. 3 : 2Answer
  2. B
    3 : 5
  3. C
    9 : 8
  4. D
    7 : 6
  5. E
    2 : 3

Answer

3 : 2
In Alloy Z, the total weight of 260 pounds is divided into 13 equal parts of 20 pounds each. Thus, copper accounts for 7 parts (140 pounds) and zinc accounts for 6 parts (120 pounds). Adding 40 pounds of pure copper increases the copper content to 180 pounds, while zinc remains at 120 pounds. Comparing copper to zinc yields 180 : 120, which simplifies to 3 : 2.

Step-by-Step Solution

1
Determine total ratio parts for Alloy Z.
The total number of ratio parts is 7+6=137 + 6 = 13 parts.
To find the weight of each component from a part-to-part ratio, divide the total weight by total ratio parts.
2
Calculate initial weights of copper and zinc in Alloy Z.
Copper weight =260×713=140= 260 \times \frac{7}{13} = 140 pounds; Zinc weight =260×613=120= 260 \times \frac{6}{13} = 120 pounds.
Multiply total weight by each component's fraction of the total.
3
Update component weights after adding pure copper.
New copper weight =140+40=180= 140 + 40 = 180 pounds; Zinc weight remains 120120 pounds.
Only copper is added to the mixture, leaving zinc weight unchanged.
4
Compute and simplify the final ratio of copper to zinc for Alloy W.
Ratio of copper to zinc =180:120=3:2= 180 : 120 = 3 : 2.
Divide both terms by their greatest common divisor, 60.

Key Concept

Ratios and Component Mixture Adjustment
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Topics

Ratios, Rates, and Proportions

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