Question 1094236: Find three consecutive even integers such that the sum of the least integer and the middle integer is 44 more than the greatest integer.
Answer by abdulimad2(2)   (Show Source):
You can put this solution on YOUR website! First of all, when approaching a question involving consecutive integers, do NOT try to substitute these consecutive integers with numerical values because it's going to take too long, and it won't be productive (in most cases). Instead, use algebra to list your integers, and then form the appropriate equation(s) from the info. given in the question.
Here, we're given that there are three consecutive EVEN integers, in which the sum of the least one and the middle one exceed the value of the greatest one by 44. Before writing an equation, we must first determine our three integers, and to do that, we will give the least integer the value x. Since even (or odd) numbers have a common difference of two (example: 2, 4, 6 have a difference of two between each of them), we'll be adding two to the least number to get to the next one. So, this makes the next term x+2, and the greatest term (x+2)+2, which is x+4. Now that we know that our three terms are x, x+2, and x+4, we'll follow the question so that we can build our equation. The sum of our least and middle terms, which is x+(x+2), is 44 more than the greatest term, x+4, yielding the following equation:
x+x+2 = x+4+44
When combining like terms and letting the variable x alone on the left side of the equation, we get the following:
2x+2 = x+48 (combining like terms)
=> 2x+2-2=x+48-2
=> 2x = x+46
=> 2x-x = 46
=> x = 46
Now that we found the value of x in the equation, all that we have to do to find the values of our three integers is to substitute 46 with x in their expressions.
x (expression for the least integer) = 46
x+2 (expression for middle integer) = 46+2 = 48
x+4 (expression for greatest integer) = 46 + 4 = 50
So, our three consecutive even integers are 46, 48, 50, and the least and middle numbers, which add up to 94, exceed the value of the largest integer (50) by 44 (because 94 - 50 = 44).
HOPE THAT HELPS!
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