The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of the three numbers is 27, what is the value of a?  Choose the correct choice from the following choices:
A) 18  B) 20  C) 21  D) 22  E) 24
Let a=2k, b=3k, and c=4k.   a+b+c = 2k+3k+4k = 9k   Since the average is 27:   9k/3 2 +3 +4= 
<gadget id="calculator">2 +3 +4</gadget>
<output>9</output>
9k   Since the average is 27:   9k/3= 27   3k = 27   k=9   Then a=18.   The answer is 18.
<result>A</result>
The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of the three numbers is 27, what is the value of a?