x is directly proportional to y and inversely proportional to z. If x = 9...

JAMB 1979

x is directly proportional to y and inversely proportional to z. If x = 9 when y = 24 and z = 8, what is the value of x when y = 5 and z = 6?

A. \(\frac{5}{6}\)
B. 11
C. 3\(\frac{3}{5}\)
D. 2\(\frac{1}{2}\)
E. 1\(\frac{1}{5}\)

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Correct Answer: Option D

Explanation

x \(\alpha\) y = x \(\alpha\) \(\frac{1}{z}\)

x \(\alpha\) \(\frac{1}{z}\)

x = k \(\frac{y}{z}\)

k = \(\frac{xz}{y}\) = \(\frac{9 \times 8}{24}\)

= 3

x = \(\frac{xz}{y}\)

= \(\frac{3 \times 5}{6}\)

= \(\frac{15}{6}\)

= \(\frac{5}{2}\)

= 2\(\frac{1}{2}\)

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