x varies directly as y and inversely as z. When y = 1.5 and z = 2, then x = 5.…
2023
x varies directly as y and inversely as z. When y = 1.5 and z = 2, then x = 5. If z = 2.5 and y = 9, then what is the value of x?
- A.
24
- B.
20
- C.
15
- D.
12
Attempted by 126 students.
Show answer & explanation
Correct answer: A
Solution: x varies directly as y and inversely as z, so x = k*y/z.
Use the given values to find k: when y = 1.5, z = 2, x = 5, so 5 = k*(1.5)/2.
Solve for k: k = 5*2/1.5 = 10/1.5 = 20/3.
Now compute x for y = 9 and z = 2.5: x = k*y/z = (20/3)*9/2.5 = (20*9)/(3*2.5) = 180/7.5 = 24.
Final answer: 24