Answer: The total boats in the marina are 105.
Step-by-step explanation:
Let the total number of boats in the marina = x
Given : Number of white boats in the marina = [tex]\frac{2}{3}x[/tex]
Number of blue boats in the marina = [tex]\frac{4}{7}\times (x-\frac{2x}{3})=\frac{4}{7}\times \frac{x}{3}=\frac{4x}{21}[/tex]
Number of red boats in the marina = [tex]x-\frac{2x}{3}-\frac{4x}{21}=\frac{3x}{21}[/tex]
Given : Number of red boats in the marina = 15
[tex]\frac{3}{21}\times x=15[/tex]
[tex]x=105[/tex]
Thus total boats in the marina are 105.
By working with fractions and proportions, we will see that there are 105 boats in the marina.
Let's say that there are N boats in the marina, we know that:
2/3 of these are white, then the proportion of boats that are not white is:
1 - 2/3 = 3/3 - 2/3 = 1/3.
Of these, 4/7 are blue, then the proportion of red ones is:
1 - 4/7 = 7/7 - 4/7 = 3/7
The total proportion of red boats is:
(3/7)*(1/3) = 1/7
And we know that there are 15 red boats, this means that:
(1/7)*N = 15
Solving for N we get:
N = 7*15 = 105
So there are 105 boats in the marina.
If you want to learn more about fractions, you can read:
https://brainly.com/question/11562149
