Alice is thinking of two numbers. When she adds them she gets 64. When she multiplies them she gets 735. What are her two numbers?

x+y=64 ---->y = 64-x

xy = 735

x(64-x) = 735
64x - x^2 - 735 = 0
x^2 - 64x + 735 = 0
(x-49)(x-15) = 0
x = 49 or x = 15

One is 49, the other is 15