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The product of two consecutive integers is two hundred forty. Find the two integers.

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  1. The square root of 240 = 15.49

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    Ms. Sue
  2. 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:
    (x-15)(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~ :)

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