SOLUTION: If one-half a number is subtracted from five-sixths of the number, the difference is 6. Find the number. Help. Thank you.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If one-half a number is subtracted from five-sixths of the number, the difference is 6. Find the number. Help. Thank you.      Log On


   

Question 29907: If one-half a number is subtracted from five-sixths of the number, the difference is 6. Find the number.

Help. Thank you.
Found 3 solutions by Cintchr, Earlsdon, sdmmadam@yahoo.com:
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
one-half a number +1x%2F2+
five-sixths of the number +5x%2F6+
+5x%2F6+-+1x%2F2+=+6+ make all fractions have a common denom of 6
+5x%2F6+-+%281x%2F2%29%283%2F3%29+=+6%286%2F6%29+
+5x%2F6+-+3x%2F6+=+36%2F6+ since all denoms are 6 and it is an equation, drop the denom.
+5x+-+3x+=+36+ combine like terms
+2x+=+36+ divide by 2
+x+=+18+
Plug back in to check
+5%2818%29%2F6+-+1%2818%29%2F2+=+6+
+90%2F6+-+18%2F2+=+6+ reduce the fractions
+15+-+9+=+6+
+6+=+6+ YES!!!

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = the number.
%285%2F6%29n+-+%281%2F2%29n+=+6 Simplify.
n%28%285%2F6%29+-+%283%2F6%29%29+=+6
n%282%2F6%29+=+6
n%281%2F3%29+=+6 Multiply both sides by 3.
n+=+18

Answer by sdmmadam@yahoo.com(530) About Me  (Show Source):
You can put this solution on YOUR website!
If one-half a number is subtracted from five-sixths of the number, the difference is 6. Find the number.
Let the number be N
one-half a number subtracted from five-sixths of the number,
the difference is 6.
(1/2) of N subtracted from (5/6) of N, the difference is 6
That is (5/6)N - (1/2)N = 6 ----(1)
That is [5/6-1/2]N = 6
Multiplying by 6 through out
(5-3)N= 36
2N = 36
N = 36/2 = 18
Answer:The required number is 18
Verification:N =18 in (1) gives LHS = (5/6)X18 - (1/2)X18 = 15-9 =6 =RHS