If 1 : x = x : y = y : 8 What is the value of x + y : y?
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If 1 : x = x : y = y : 8
What is the value of x + y : y? Assume that x and y are both positive integers.
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Answer: C. C) 3 : 2
From 1/x = x/y, y = x^2. From x/y = y/8, y^2 = 8x. Substituting yields x^4 = 8x => x = 2, y = 4. Then (x + y) : y = (2 + 4) : 4 = 6 : 4 = 3 : 2.
Step-by-step Derivation:
Step 1: Given 1/x = x/y => y = x^2.
Step 2: Given x/y = y/8 => y^2 = 8x.
Step 3: Substitute y = x^2: (x^2)^2 = 8x => x^4 = 8x.
Step 4: For positive integers, divide by x: x^3 = 8 => x = 2.
Step 5: Then y = 2^2 = 4.
Step 6: Compute (x + y) : y = (2 + 4) : 4 = 6 : 4 = 3 : 2.