Find three consecutive integers such that the sum of the second and third is 89.

Answer 1

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