SOLUTION: Find two consecutive integers such that three times the larger is 22 more than twice the smaller.

Question 926507: Find two consecutive integers such that three times the larger is 22 more than twice the smaller.
Answer by EMStelley(208) (Show Source): You can put this solution on YOUR website!
The first step to solving a problem like this is to name your variable. In this case, our unknown happens to be the two consecutive integers. Let's call the first one x. Then by the definition of consecutive, the other one would be x+1.
Now, we must deal with "such that three times the larger is 22 more than twice the smaller." Note that "three times the larger" is implying 3(x+1) since x+1 is larger than x. And "22 more than twice the smaller" would mean 2x+22. Note that the use of "is" in a word problems refers to the equal sign.
So putting it all together, we have:

Distributing the left hand side we get:

Subtracting the 3 from both sides results in:

Subtracting 2x from both sides results in:

So we now know that our first number is 19. Then the other number was x+1, so it would be 20! So the answer here is 19 and 20.
I hope that helps!
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