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An alloy of copper and bronze weighs 50 g and contains 80% copper by weight. How much pure copper (in grams) should be added to this alloy so that the percentage of copper increases to 90% by weight (assume the added material is 100% copper)?

Difficulty: Medium

Correct Answer: 50 g

Explanation:


Introduction / Context:
This problem tests mixture percentage adjustment by adding a pure component. When you add pure copper, only the copper part increases while bronze remains unchanged. The new copper percentage is found by setting (new copper)/(new total weight) = target percentage.


Given Data / Assumptions:

  • Total alloy weight initially = 50 g
  • Initial copper percentage = 80%
  • Target copper percentage = 90%
  • Added copper is pure (100% copper)


Concept / Approach:
Find initial copper weight, add x grams copper, and solve (copper + x)/(total + x) = 0.90.


Step-by-Step Solution:

Step 1: Initial copper = 80% of 50 = 0.80 * 50 = 40 g Step 2: Initial bronze = 50 - 40 = 10 g (this stays fixed) Step 3: Let added copper = x g Step 4: New copper = 40 + x; new total = 50 + x Step 5: Target condition: (40 + x)/(50 + x) = 0.90 Step 6: 40 + x = 0.90(50 + x) = 45 + 0.90x Step 7: x - 0.90x = 45 - 40 => 0.10x = 5 => x = 50


Verification / Alternative check:
After adding 50 g, total = 100 g and copper = 90 g. Copper% = 90/100 = 90%. Verified.


Why Other Options Are Wrong:

45 g: copper% = 85/95 ≈ 89.47%, not 90%. 10 g: copper% = 50/60 = 83.33%, too low. 25 g: copper% = 65/75 ≈ 86.67%, too low. 60 g: copper% = 100/110 ≈ 90.91%, too high.


Common Pitfalls:
Some students mistakenly increase copper percentage by adding 10% of 50 (5 g), ignoring the denominator change. Another mistake is using 90% of the old weight instead of the new total weight (50 + x).


Final Answer:
50 g

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