3/4 of the boats are white, 4/7 are blue, and the rest are red and if 9 boats are red how many is there

3/4 of all boats in the marina are white. Therefore, the remaining 1/4 of boats are not white. From the 1/4 of non-white boats, 4/7 of them are blue. That means that 3/7 of the 1/4 non-white boats are red. We know that summing up all fractions of boat colors should give us a value of 1, shown below.
fraction of white boats + fraction of blue boats + fraction of red boats = 1
3/4 + 1/4(4/7) + 1/4(3/7) = 1

The fraction of red boats out of all boats is 1/4(3/7) or 3/28.

If we let the variable T = total number of boats and R = number of red boats, the number of red boats over total should equal the fraction of red boats, R/T = 3/28.

Plugging in R = 9, we can solve for the total number of boats in the marina.
R/T = 3/28
9/T = 3/28
9 = 3T/28
9*28/3 = T
T = 84

There are 84 boats in the marina.