Question

There are two numbers whose sum is 30 and whose product is 221. This number differ by

(A) 4
(B) 3
(C) 2
(D) 1

Answer 1

A

Answer 2

First problem: Call the numbers x and y

Then:
x + y = 30
xy = 221

y = 30 - x (subtract x from each side of first equation)
x(30 - x) = 221 (substitute 30-x for y in second equation)
30x - x^2 = 221 distributive property of multiplication over addition
-x^2 + 30x = 221 re-arrange terms on left side
-x^2 + 30x - 221 = 0 subtract 221 from each side

Feed the coefficients into the quadratic formula to find that x = 13 or 17,
so the two numbers differ by 4.

Answer 3

oh...okay.