SOLUTION: When one half of the second of two consecutive integers is subtracted from the first of the two consecutive integers, the result is 2.

Question 115230: When one half of the second of two consecutive integers is subtracted from the first of the two consecutive integers, the result is 2.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Since the two integers are consecutive, if we call the first one X, then the second one
will be 1 number bigger, so it will be X + 1.
.
One-half of the second integer is (1/2)*(X + 1). If you subtract this from the first integer
X the answer is to be 2. In equation form this is:
.
X - (1/2)(X + 1) = 2
.
You can get rid of the fraction (1/2) by multiplying both sides of this equation (all terms) by
2 and the equation becomes:
.
2X - (X + 1) = 4
.
Since the parentheses are preceded by a minus sign, you can remove the parentheses if
you change the signs of the terms inside the parentheses. Applying this rule results in:
.
2X - X - 1 = 4
.
Get rid of the -1 on the left side by adding +1 to both sides and you have:
.
2X - X = 5
.
Combine the two terms on the left side and you have:
.
X = 5
.
This tells you that the two consecutive integers are 5 and 6
.
Check. If you take half of the second integer you get 3. And if you subtract that from
the first integer you get 5 - 3 = 2 ... which is just what the problem required. Therefore,
the answer that the integers are 5 and 6 checks out.
.
Hope this helps you to understand how to work the problem.
.

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