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