11.BONUS: What is the largest of three consecutive positive integers if the sum of the smaller two integers is 11?

Answer 1

Let x = the smallest positive integer. Since the other two are consecutive, they must be x+1 and x+2. The sum of the smaller two is 11:

x + x+1 = 11

2x + 1 = 11

Solve for x, the smallest integer. Once you have the value of x, the largest integer is x+2.

Answer 2

Let n be the largest of three consecutive numbers. Then the number just smaller is (n - 1) and the number smaller than that is (n - 2). So, since the sum of the two smallest numbers is 11, then (n - 1) + (n - 2) = 11 or, combining like-terms, 2n - 3 = 11. Add 3 to both sides to get 2n = 14 then divide both sides by 2 to get n = 7

So the largest number is 7, the other two numbers are 5 and 6.