Question 99332: The sum of 2 consecutive integers is 250. Identify BOTH of the numbers. The formula must construct an algebraic equation with a variable.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! I suspect that you have an error in the way you stated your problem. There are NO two integers
that are consecutive and add up to 250.
.
The way to express two consecutive integers is to let the smaller one be represented
by x. The next integer up from it is x + 1. The problem says that these two
integers
are to total 250 when added. In equation form this means that:
.
x + x + 1 = 250
.
Combine the two x's on the left side to make the equation become:
.
2x + 1 = 250
.
Get rid of the +1 on the left side by subtracting +1 from both sides to reduce the equation
to:
.
2x = 249
.
Solve for x by dividing both sides of this equation by 2 ... the multiplier of x to get:
.
x = 249/2 = 124.5
.
This doesn't work out to be a whole number. 124 and 125 are two consecutive integers
but they add to be 249. And 125 and 126 are the next pair of consecutive integers,
but they add to 251. So there is no solution.
.
But if you had said to find two consecutive EVEN integers, then there would be a solution.
Represent the smaller integer by x. Then the next even integer would be 2 above that so it
would be x + 2. [Think in terms of 4 as an even integer. The next even integer is 6 and
it is equal to 4 + 2.]
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Now when you add the two even integers the equation becomes:
.
x + x + 2 = 250
.
Combine the two x's on the left side to get:
.
2x + 2 = 250
.
Get rid of the +2 on the left side by subtracting 2 from both sides to make the equation:
.
2x = 248
.
Solve for x by dividing both sides by 2 to reduce the equation to:
.
x = 124
.
And, since the next even integer is 2 above that number, it is 126. This works because
124 plus 126 does equal 250.
.
Hope this discussion helps you to find your mistake in the problem and shows you the process
that you use to solve problems such as these.
.
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