The product of two consecutive odd numbers is 399. What are the numbers?

The product of two consecutive odd numbers is 399. What are the numbers?

Detailed Explanation

The fastest way to solve this would be to simply multiply the possible choices together (19 × 21 = 399). You can also solve this with algebra. Let x equal the first number and x + 2 the second number.

x(x + 2) = 399

\(x^2 + 2x = 399\) (Note: This is a quadratic equation that can be solved by setting it equal to zero and factoring.)

\(x^2 + 2x - 399 = 0\)

(x – 19)(x + 21) = 0

x – 19 = 0 or x + 21 = 0

x = 19 or x = –21

x + 2 = 21 or x + 2 = –19

Two solutions are possible: 19 and 21, and –21 and –19. Because the latter pair isn’t one of the answer choices, the first pair is the correct answer.

x(x + 2) = 399

\(x^2 + 2x = 399\) (Note: This is a quadratic equation that can be solved by setting it equal to zero and factoring.)

\(x^2 + 2x - 399 = 0\)

(x – 19)(x + 21) = 0

x – 19 = 0 or x + 21 = 0

x = 19 or x = –21

x + 2 = 21 or x + 2 = –19

Two solutions are possible: 19 and 21, and –21 and –19. Because the latter pair isn’t one of the answer choices, the first pair is the correct answer.