the sum of three consecutive even integers is at least 80 and at most 90. what is the largest possible combination of these three integers?
The sum of 3 consecutive even integers is at least 80 and at most
Call the first number X. The second will be X+2 (the next even number). The third is (X+2)+2=X+4. So the sum is X+X+2+X+4= 3X+6
So we now have 80 ≤ 3x+6 ≤ 90
80 -6≤ 3X+6-6≤ 90-6
74≤ 3X≤ 84
74/3≤ 3X/3≤ 84/3
24.666≤ X≤ 28
Since we know X is an even integer, the only options we have are 26 and 28.
We already said the X is the smallest number, and the next two are X+2 and X+4. Plugging in the 2 options for x, we have two possible solutions.
1) 26+28+30= 84