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\(\frac{1}{5}\)
Correct Answer: 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\(\frac{1}{2}\)
