Question

R varies partly as x and parly as the square of y. R=21 when x=y=1 and R=48 when x=y=2.Express R. in terms of x and y.

Answer 1

R = a(x) + b(y^2)

case 1: R = 21, x = y = 1
21 = a + b

case 2: R = 48, x = y = 2
48 = 2a + 4b
or 24 = a + 2b

subtract them:
3 = b
then in a+b=21, a = 18

R = 18x + 3y^2

Answer 2

REiny is right