math
posted by Karina .
The product of two consecutive integers is two hundred forty. Find the two integers.

The square root of 240 = 15.49

first represent unknowns using variables,,
let x = first number
let x+1 = second number
note that the second number is x+1 because they are consecutive numbers.
now we set up the equation,, according to problem, their product is 240, thus:
x(x+1) = 240
x^2 + x = 240
x^2 + x  240 = 0
to solve for x, we can either factor it (if it's factorable) or use quadratic formula. since it's factorable, let's just factor this:
(x15)(x+16) = 0
x = 15 and x = 16
thus there are 2 pairs of answers:
(i) x = 15 and x+1 = 16 ; and
(ii) x = 16 and x+1 = 15
hope this helps~ :)