Question 512744: Find two consecutive even integers such that the sum of the larger and 3 times the smaller is 234.
As far as I got was x+3x=234 but then I got stuck and was not even sure that was right.
Found 2 solutions by scott8148, bucky:
Answer by scott8148(6628)   (Show Source):
Answer by bucky(2189)  (Show Source):
You can put this solution on YOUR website! Let's first think about consecutive even integers. For example think of these consecutive even integers: 12, 14, 16, 18, 20 ... Notice that that there is a difference of 2 between consecutive even integers. Therefore, if X represents the smaller of two consecutive even integers, then the next even integer in the series would be represented as X + 2.
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So, we can say that X represents the smaller integer in a series of even integers and X + 2 represents the next bigger even integer.
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The problem tells you that the sum of the larger (X + 2) and 3 times the smaller (3 times X or just 3X) equals 234. So we can write the equation:
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X + 2 + 3X = 234
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Eliminate the 2 on the left side by subtracting 2 from BOTH sides. When you do the subtraction of 2 from BOTH the left and the right sides, the equation reduces to:
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X + 3X = 232
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Combine the X terms on the left side by adding them:
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4X = 232
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Solve for X by dividing BOTH sides by 4 to get:
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X = 232/4 = 58
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Since X = 58 and X represents the smaller of the 2 even numbers, the next larger consecutive even number is 60. The two consecutive even numbers you are looking for are 58 and 60.
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Check by adding the larger (60) to 3 times the smaller (3*58). 3 times 58 is 174. Add 60 to 174 and you get 234. That checks out, so our answers 58 and 60 are correct.
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Hope this helps you to understand the problem a little better. You were close with your equation, but you used X to represent both the smaller and the larger number. Your equation would have reduced to:
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4X = 234
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and when you divide both sides by 4 to solve for X, you would find that 4 does not divide evenly into 234. The answer would have been that X = 58 and a half and that would not be correct. The answer should be an integer (whole number).
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