Number Properties Puzzle – Challenge 13
Number Properties Puzzle – Challenge 13 gives t and √w as inversely proportional, with t = 2 when w = 9, and asks for t when w = 2. Inverse proportion means their product is constant, so the whole puzzle reduces to finding that constant and rationalizing the result.
Challenge:
If t and \(\sqrt{w}\) are inversely proportional when t = 2 and w=9, what is the value of t when w =2?
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The correct answer is \(3\sqrt{2}\).
t and \(\sqrt{w} \) are inversely proportional when t = 2 and w=9,
Then, \(t × \sqrt{w} = 2 × \sqrt{9} = 2 × 3 = 6\)
w =2, then,
\(t × \sqrt{w} = 6 → t × \sqrt{2} = 6 → t = \frac{6}{\sqrt{2}} × \frac{\sqrt{2}}{\sqrt{2}} = \frac{6\sqrt{2}}{2} = 3\sqrt{2}\)
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