Question 603325: I think of a number. I double it, add 120 and then add the number i first thought of. The answer is 360. What is the number?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! You think of a number. Let's call that number N.
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You double it. That means that you multiply it by 2. So now you have 2N
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Next you add 120 to the 2N you have. When you do that you have 2N + 120
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Then you add to this amount the number you first thought of (which was N) and you get:
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2N + 120 + N
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Notice that you can combine the 2N and the +N to get a total of 3N. So after combining these two terms that both contain N your expression simplifies to:
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3N + 120
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Finally, you know that this amount is equal to 360. This means that you can write this equality as:
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3N + 120 = 360
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To solve this equation, we need to get just an N by itself on the left side. So we can start by getting rid of the 120 on the left side. We can do that by subtracting 120 from the left side. But whatever we do to the left side, we must also do to the right side so that we keep both sides equal. So we need to subtract 120 from both sides. It looks like this:
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3N + 120 - 120 = 360 - 120
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On the left side the + 120 and the -120 cancel each other. The answer is zero and we don't need to write the zero. And on the right side the 360 minus 120 is 240. So we have simplified the equation to:
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3N = 240
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Remember that we are trying to get just N on the left side. There are 3 of N on the left side. So to get just one N we can divide the left side by 3. But when we divide the left side by 3, we must also divide the right side by 3 to keep both sides equal. Dividing the 3N by 3 results in just N on the left side, and dividing the 240 by 3 on the right side gives an answer of 80. This means that we have reduced the equation to:
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N = 80
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and that says that N, the number we originally thought of, is equal to 80. That's the answer to this problem. Let's check it:
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We start with 80. Then we double it to get 160. Then we add 120 and we have 280. Then we add the original number to that amount and we get 280 + 80 = 360. That is exactly the answer that, according to the problem, it should be. So our answer of 80 is correct.
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Hope this helps you understand what the problem was asking and a way that you can work it out to find the answer.
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