if y=6 when x=2/3 find x when y=12

Question

Assume that y varies directly with x, then solve. Simplify completely. The answer is a fraction.

Answer 1

If y varies directly as x then

y = kx, where k is the constant of variation.

y = 6 when x = 2/3 so

6 = k*2/3

3/2*6 = k*2/3*3/2

9 = k

so y = 9x

when y = 12

12 = 9x

x = 12/9 = 4/3