word problem

Question

Three quarters of the boats in the marina are white, 4/7 of the remaining boats are blue, adn the rest are red.  If there are 9 red boats, how many boats are in the marina?

Answer 1

Let x = the number of boats in the marina:

• Three quarters of the boats in the marina are white: (3/4)x
• 4/7 of the remaining boats (1/4) are blue: (4/7)*(1/4) = (1/7)x
• The rest are red

 

The white and blue boats accounts for (3/4)x + (1/7)x = (21/28)x + (4/28)x = (25/28)x.  So the red boats account for the remaining x - (25/28)x = (3/28)x of the boats.  If there are 9 red boats, then:

 

     (3/28)x = 9

     x = 9*(28/3)

     x = 84 boats