determine three consecutive integers ?

Question

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.

Answer 1

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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?

Answer 2

(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?