Algebra Question

Question

The sum of 3 consecutive integers is 27 less than the least of the integers..

What's the smallest and largest integers?

Answer 1

Answer 2

We need a way to communicate "three consecutive integers" with math. One approach could be to call the smallest of the integers n so that the other integers would be n+1 and n+2. Another could be to call the middle of the three x, making the smallest be x-1 and the largest be x+1. There are more but choose whichever you feel most comfortable with.

Once we establish what makes up our consecutive integers, we can sum them as the problem states (this parts easy, just add them together).

The last bit of the problem statement is that this sum should be equal to 27 less than the smallest of the three integers. To express this, take whatever you chose to express the smallest of the three (in the examples I gave, this would be n or x-1) and subtract 27 from it. You should now have a relatively simple equation in terms of one variable that you can solve.

A similar example problem:

The sum of 2 consecutive even integers is 3 times the smaller integer. What is the larger integer?

Let n be the smaller even integer and n+2 be the larger even integer, then

n + (n + 2) = 3n

-> 2n + 2 = 3n

-> 2 = n

Thus the larger even integer is 4.