Question

Suppose that r varies directly with s and inversely with t, and r = 2 when s = 3 and t = 12. What is the value of r when s = 5 and t = 4?
A. 2/5
B.32/5
C.10
D.20

Answer 1

The statement suppose that r varies directly with s and inversely with t is best represented as:

r α s/t

To make it into equality, we insert a proportionality constant, k:

r = ks/t

Using the initial conditions, we solve for k.

r = ks/t
r = 2 when s = 3 and t = 12

2 = k(3)/12
k = 8

Thus, when s = 5 and t = 4,

r = 8(5)/4
r = 10 -----> OPTION C