The key to this question is in understanding the definition of the terms.
An integer is a whole number, i.e. 1, 14, 27 and so on.
Consecutive means the numbers are in counting order, or one right after the other, such as 1, 2, 3 and so on.
Now with this problem we do not know the value of the integers to start so we must start with a variable. Let's call our starting variable x.
If our starting value is x, then the consecutive integer after that would be x+1 and the integer after that would be x+2
*** Remember our example of integers 1,2,3. In this example 1 is the starting integer. The first consecutive integer is (1 + 1) or 2. The next consecutive integer is (1 + 2) which equals 3***
So, our question wants us to find 3 consecutive integers such that the sum of the second and third is 89.
With our starting variable as x we know that the second consecutive integer is x+1 and the third is x+2.
When we write that in an equation we get (x+1) + (x+2) = 89
Then we solve for x:
x + 1 + x + 2 = 89
2x + 3 = 89
2x = 86
x = 43
Now we plug x back into our integer equations
Our first integer was x which equals 43
Our second integer was x + 1 which equals 44
Our third integer was x + 2 which equals 45
So, our answer is three consecutive integers such that the sum of the second and third is 89 are
43, 44, 45