## Trending News

# 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

- PuzzlingLv 72 months agoFavorite 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?

- rotchmLv 72 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?