Question 81746: some help would be wonderful.Thanks
One number is 12 more than another. The sum of the smaller number and twice the larger number is 39. Find the larger number.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let "one number" be represented by x. Then "the other number" is 12 more than it. So that
number [which is the bigger number] is x + 12.
.
So you have the two numbers of x and x + 12
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Next you are told that if you add the smaller number [x] to twice the larger number [2*(x+12)]
the answer is 39. In equation form this becomes:
.
x + 2*(x + 12) = 39
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Do the distributed multiplication on the left side by multiplying 2 times each of the terms
in the parentheses. When you do, the equation becomes:
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x + 2x + 24 = 39
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Combine the two terms on the left side that each contain an "x". When you add them the
equation becomes:
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3x + 24 = 39
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Next get rid of the 24 on the left side by subtracting 24 from both sides of this equation.
Subtracting 24 from both sides results in:
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3x = 15
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Finally solve for x by dividing both sides of this equation by the multiplier of x (the
multiplier is 3, so divide both sides by 3) and you get:
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x = 5
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You were asked to find the bigger of the two numbers. You now know that the smaller
number (x) is 5 and the problem tells you that the bigger number is 12 more than that.
So the bigger number is 5 + 12 or 17.
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The two numbers are 5 and 17.
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Check ... does the smaller number plus twice the bigger number add up to be 39? Twice the
bigger number is 2 times 17 or 34 and then adding the smaller number to that you get:
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5 + 34
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and that does, in fact, add up to 39 just as the problem required. So the answer checks
out correctly.
.
Hope this helps you to understand this problem a little better.
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