So 1/2 < y/(x + y) < 1 multiply all sides by 10: 1/2 × 10 < y/(x + y) × 10 < 1 × 10 add 10 10 + 1/2 × 10 < 10 + y/(x + y) × 10 < 10 + 1 × 10 We see that we have the expression for k in the middle, therefore:
15 < k < 20
The only answer choice that fits is (D).
The main ideas we use are following: - proper transformation of the expression for k - evaluation of y/(x + y) based on fact that 0 < x < y.
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