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

Question

I don't understand what someone put before with all the numbers can someone please help me .

Answer 1

Hello!

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.

Answer 2

.75boats/white

.25*4/7=boats/blue

.25*3/7=boats/red=9=3/7*1/4

3=1/7*1/4

3=1/28

84boats

.75*84=63are white

9 red (given)

12 blue