Step-by-step explanation:
The sum of three consecutive even integers is 390. What are the integers?
In order to ensure the numbers are even I generally call the first
integer 2n because 2 multiplied by any number will always be even.
Our consecutive even integers are: 2n, 2n+2, 2n+4
2n + 2n+2 + 2n+4 = 390
6n + 6 = 390
6n = 384
n = 64
Our 1st integer is 2n = 2(64) = 128
Our integers are 128, 130, 132
Check: 128+130+132 = 390 which is correct.
2) The sum of three consecutive odd integers is 99. What are the integers?
Same logic applies: An odd integer will always result from 2n+1
So we will call our 3 consecutive odd integers 2n+1, 2n+3, 2n+5
2n+1 + 2n+3 + 2n+5 = 99
6n+9 = 99
6n = 90
n = 15
Our first odd integer is 2n+1 = 2(15) + 1 = 31
Our 3 consecutive odd integers are 31, 33, 35
Check: 31 +33+45 = 99 Yes
3)Which equation defines three consecutive odd integers that add up to 81?
A) n(n+1)(n+2)=81
B) n(n+2)(n+4)=81
C) n+(n+1)+(n+3)=81
D) n+(n+1)+(n+2)=81
E) n+(n+2)+(n+4)=81
We can immediately discard answers A, B because they are multiplying
instead of adding.
That leaves C, D, E
This question does not follow the logic I utilized in question 1 and 2.
Assuming the first number is indeed odd and is called n
The next odd number is n+2 followed by n+4
Thus we must have: n + (n+2) + (n+4) = 81
The answer is E
By the way: The numbers are 25, 27, 29
