Y varies jointly as a and b and inversely as the squareroot

Y varies jointly as a and b, and inversely as the squareroot of c. y = 80 when a = 5, b = 8, and c = 9. Find y when a = 8, b = 6, and c = 36. y =

Solution

Since y varies jointly as a and b and inversely as square root of c, let y = kab/c , where k is the constant of proportionality. Further, since y = 80, when a = 5, b= 8 and c = 9, therefore, 80 = k*5*8 /9 = 40k/3 so that k = 80*3/40 = 6. Then y = 6ab/c. Now, when a = 8, b=6 and c = 36, we have y = 6*8*6/36 = 288/6 = 48. The answer is 48.