Some Easy Math I'm too Lazy to Do

Question

There are white, blue, and red boats in a marina. Two-thirds of the boats in the marina are white,
4/7 of the remaining boats are blue, and the rest are red. If there are 15 red boats, how many boats are in the marina?

Answer 1

There are a total of x boats in the marina.

 

"There are white, blue, and red boats in a marina"   means white + blue + red = x

 

Number of white:

  "Two-thirds of the boats in the marina are white"     means    (2/3)x

 

Number of blue:
 "4/7 of the remaining boats are blue"   means    (4/7)(x - (2/3)x)  or   (4/7)(1/3)x = (4/21)x

 

Number of red:

  "the rest are red" and "15 red boats"  means  (2/3)x + (4/21)x + 15 = x

 

(2/3)x + (4/21)x + 15 = x

  14x + 4x + 315 = 21x         [multiply by LCM of 21]

       315 = 3x

       105 = x

 

Check:

    Does    (2/3)(105) + (1/3)(105) + 15 = 105   ?

                  70 + 35 = 105   ?

                   105 = 105   ?yes