determine three consecutive integers ?

determine three consecutive integers so that the product of the two largest numbers is 200 more than the product of the two smallest numbers.

The answer is going to be: 99, 100, 101. 

Can someone show me step by step how I can get those answers? Thank you.

2 Answers

  • 2 months ago
    Favorite Answer

    Hint: Let x be the middle integer. The one before will be x-1 and the one after will be x+1.

    The product of the larger pair is x(x+1)

    The product of the smaller pair is x(x-1)

    Create an equation:

    x(x+1) = x(x-1) + 200

    Expand that and you get:

    x² + x = x² - x + 200

    The x² terms cancel out and you have a simple linear equation.

    Do you see now how to get to the answer?

  • rotchm
    Lv 7
    2 months ago

    (n-1), n, (n+1)

    n(n+1) = 200 + (n-1)n.

    Expand & rewrite. This is a quadratic in n, so you can solve for n (via quadratic eqs or plain ol' factoring). Can you do these parts?

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