SOLUTION: If one-half thenumber is subtracted from five-sixths of the number,the difference is 6. Find the number

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Question 77316: If one-half thenumber is subtracted from five-sixths of the number,the difference is 6. Find the number
Found 2 solutions by checkley75, jim_thompson5910:
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
5x/6-x/2=6
(5x-3x)/6=6 cross multiply
5x-3x=36
2x=36
x=36/2
x=18 answer
proof
18(5/6)-18/2=6
90/6-9=6
15-9=6
6=6

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=the unknown number
So we have
%285%2F6%29x-%281%2F2%29x=6
%285%2F6%29x-%283%2F3%29%281%2F2%29x=6 Multiply the 2nd term by (3/3) to get the LCD
%285%2F6%29x-%283%2F6%29x=6
%28%285-3%29%2F6%29x=6
%282%2F6%29x=6
x=6%286%2F2%29 Multiply both sides by (6/2)
x=18
So the number is 18


Check:
%285%2F6%29x-%281%2F2%29x=6 plug in x=18
%285%2F6%29%2818%29-%281%2F2%29%2818%29=6
15-9=6
6=6 works