Discussion
x varies directly with y when z is constant and varies directly with z when y is constant. When y = 1.5, z = 4, then x = 2.5. What is the value of x when y = 8 and z = 2.4?
Answer: C
The value of x is 8. Since x varies directly with y when z is constant and directly with z when y is constant, x = kyz for some constant k. From y = 1.5, z = 4 and x = 2.5: \[2.5 = k \times 1.5 \times 4\] so \(k = \frac{2.5}{6} = \frac{5}{12}\). For y = 8 and z = 2.4: \[x = \frac{5}{12} \times 8 \times 2.4\] \[x = \frac{5 \times 19.2}{12} = 8\] The options 5, 6 and 10 do not satisfy this relation.
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