SOLUTION: Find a number such that one-half of the number is 9 less than two-thirds of the number

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Question 491901: Find a number such that one-half of the number is 9 less than two-thirds of the number
Answer by Maths68(1474) About Me  (Show Source):
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Let x is the number
one-half of the number = (1/2)x =x/2
two-thirds of the number=(2/3)x=2x/3
Given condition
x/2=9-2x/3
x/2+2x/3=9
Taking LCM on Left hand side
[3(x)+2(2x)]/6=9
(3x+4x)/6=9
Multiply by 6 both sides
3x+4x=54
7x=54
Divide by 7 both sides
7x/7=54/7
x=54/7
So number is 54/7
Check
x/2=9-2x/3
(54/7)(1/2)=9-(54/7)(2/3)
54/14=9-(108/21)
27/7=9-(36/7)
Taking LCM on right hand side
27/7=(63-36)/7
27/7=27/7