Problem: THE SUM OF TWO WHOLE NUMBERS IS 11. THEIR PRODUCT IS 28. FIND THE TWO NUMBERS.
The sum of two whole numbers is 11. Their product is 28. Find the two numbers.
x + y = 11
xy = 28
x = 11 - y
(11 - y)y = 28
11y - y^2 = 28
-y^2 + 11y - 28 = 0
y^2 - 11y + 28 = 0
(y - 7)(y - 4) = 0
This tells us that one, or both, of the factors must be zero.
Set each to zero and solve.
y - 7 = 0
y = 7
y - 4 = 0
y = 4
Now we have:
x = 11 - y
x = 11 - 7
x = 4
x = 11 - y
x = 11 - 4
x = 7
xy = 28
7*4 = 28
28 = 28
Answer: the numbers are 7 and 4.