SOLUTION: I am a number. There's a number to the right of me on the number line and when you double it, the answer is forty-eight. There's a number exactly the same distance away from me

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Question 992169: I am a number. There's a number to the right of me on the number line and when you double it, the answer is forty-eight.
There's a number exactly the same distance away from me on the left, and when you triple it, the answer is thirty-six.
What number am I?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the unknown number
Let +n+%2B+k+ = the number to the right on number line
Let +n+-+k+ = the number to the left on number line
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Given:
(1) +2%2A%28+n%2B+k+%29+=+48+
(2) +3%2A%28+n+-+k+%29+=+36+
---------------------
(1) +2n+%2B+2k+=+48+
(2) +3n+-+3k+=+36+
-------------------
Multiply both sides of (1) by +3+
Multiply both sides of (2) by +2+
Then add the equations
(1) +6n+%2B+6k+=+3%2A48+
(2) +6n+-+6k+=+2%2A36+
---------------------
+12n+=+144+%2B+72+
+12n+=+216+
+n+=+18+
You are 18
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check:
(1) +2%2A%28+n%2B+k+%29+=+48+
(1) +2%2A%28+18%2B+k+%29+=+48+
(1) +36+%2B+2k+=+48+
(1) +2k+=+12+
(1) +k+=+6+
and
(2) +3%2A%28+n+-+k+%29+=+36+
(2) +3%2A%28+18+-+k+%29+=+36+
(2) +54+-+3k+=+36+
(2) +3k+=+18+
(2) +k+=+6+
OK