SOLUTION: The sum of an integer and the next greater integer is at least 35. Find the least pair of such integers.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The sum of an integer and the next greater integer is at least 35. Find the least pair of such integers.       Log On


   



Question 598166: The sum of an integer and the next greater integer is at least 35. Find the least pair of such integers.

Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there!
.
[I] Define variables
Let n be an integer.
Then n+1 is the next greater integer.
.
[II] Write an inequality describing the given relationship(s).
The phrase, "The sum of an integer and the next greater integer," can be written as n+(n+1).
The phrase "at least 35" can be written as "greater than or equal to 35." Together, we have
.
n%2B%28n%2B1%29%3E=35
.
Simplify and solve for n.
2n%2B1%3E=35
2n%3E=35-1
2n%3E=34
n%3E=17
.
We want the least pair of such integers. The integer 17 is the smallest integer which satisfies the equation n%3E=17. The next greater integer is 18. We see that the sum of 17 and 18 is 35, and 35 is at least 35.
.
That's it. Feel free to email via gmail if you have questions about the solution.
.
Ms.Figgy
math.in.the.vortex@gmail.com