2/3 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: 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

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