SOLUTION: the ratio of 2 less than a number to 6 more than that number, is 2 to 3. Find the number

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Question 29454: the ratio of 2 less than a number to 6 more than that number, is 2 to 3. Find the number
Found 2 solutions by Earlsdon, sdmmadam@yahoo.com:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let n be the required number. From the problem, you can write:
%28n-2%29%2F%28n%2B6%29+=+2%2F3 Multiply both sides by (n+6)
n-2+=+%282%2F3%29%28n%2B6%29 Multiply both sides by 3.
3%28n-2%29+2%28n%2B6%29 Expand.
3n-6+=+2n%2B12 Subtract 2n from both sides.
n-6+=+12 Add 6 to both sides.
n+=+18
Check:
%2818-2%29%2F%2818%2B6%29+=+16%2F24 Reduce this fraction to 2%2F3

Answer by sdmmadam@yahoo.com(530) About Me  (Show Source):
You can put this solution on YOUR website!
the ratio of 2 less than a number to 6 more than that number, is 2 to 3.
Find the number
Let the required number be N
2 less than N is (N-2)
6 more than N is (N+6)
Given that the ratio of (N-2) and (N+6) is 2/3
That is (N-2)/(N+6) = 2/3
3(N-2) =2(N+6)
3N-6=2N+12
3N-2N=12+6
N=18
Answer: The required number is 18
Verification: Ratio of (N-2) and (N+6)
=(N-2)/(N+6)
=(18-2)/(18+6)
=16/24
=(8X2)/(8X3)
=2/3 (cancelling 8 in the nr and in the dr)
which is correct