100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x kgs of an…
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100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x kgs of an alloy of tin and lead in the ratio 3:2. If the overall alloy should contain between 40% and 50% tin, what is the range of values x can take?
- A.
100 kgs ≤ x ≤ 200 kgs
- B.
80 kgs ≤ x ≤ 240 kgs
- C.
110 kgs ≤ x ≤ 220 kgs
- D.
75 kgs ≤ x ≤ 250 kgs
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Correct answer: D
Given: 100 kg of an alloy in ratio 1:3 (tin = 25%) mixed with x kg of an alloy in ratio 3:2 (tin = 60%).
Let the overall tin percentage be (25 + 0.6x)/(100 + x). We require 40% ≤ overall tin ≤ 50%.
Lower bound: (25 + 0.6x)/(100 + x) ≥ 0.4. Multiply both sides by (100 + x): 25 + 0.6x ≥ 40 + 0.4x ➜ 0.2x ≥ 15 ➜ x ≥ 75.
Upper bound: (25 + 0.6x)/(100 + x) ≤ 0.5. Multiply both sides by (100 + x): 25 + 0.6x ≤ 50 + 0.5x ➜ 0.1x ≤ 25 ➜ x ≤ 250.
Answer: 75 ≤ x ≤ 250.