NECO 2008 Mathematics · Question 9

x varies directly as y and inversely as z. when x = 5, y = 2 and z = 1. What is the value of x when y = 5 and z = 2?

Options

A.2.5
B.5
C.6.25
D.6.52
E.7.5

Answer: C. 6.25

Explanation written with AI and checked against the answer key

Analyze the question: x varies directly as y and inversely as z. This is a joint/combined variation problem. Concept: If x varies directly as y and inversely as z, then x = ky/z, where k is the constant of proportionality. Step 1: Find k When x = 5, y = 2, z = 1: 5 = k(2)/1 5 = 2k k = 5/2 = 2.5 Step 2: Use k to find x When y = 5 and z = 2: x = (2.5 × 5)/2 x = 12.5/2 x = 6.25 Check: Using the ratio method, x₂ = x₁ × (y₂/y₁) × (z₁/z₂) = 5 × (5/2) × (1/2) = 25/4 = 6.25. ✓ Answer: C. 6.25 Tip: For combined variation, write x = ky/z immediately, then find k first. Variables that vary directly go on top, and those that vary inversely go at the bottom. The ratio method is a quick way to check your answer. Be careful not to confuse 6.25 with the distractor 6.52!

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