x varies directly as the product of u and v and inversely as their sum. If x = 3 when u = 3 and v = 1, what is the value of x if u = 3 and v = 3?
A
3
B
4
C
6
D
9
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(x\propto \frac{uv}{u+v}\)
x = \(\frac{kuv}{u+v}\)
K = \(\frac{x(u+v)}{uv}\)
\(\frac{3(3+1)}{3\times1}\)
\(\frac{3\times4}{3}\)
k = 4
x =\(\frac{4uv}{u+v}\)
x = \(\frac{4\times 3\times3}{3+3}\)
x = \(\frac{36}{6}\)
x = 6
Source: Myschool Past Questions Archive (Record #7747)