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.
- 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?