Question

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

Answer 1

Answer:

84 boats are there in the marina.

Step-by-step explanation:

Given:

Three quarters of the boats are white.

4/7 of the remaining boats are blue and rest are red.

Number of red boats (r) = 9

Total number of boats = ?

Let the total number of boats be 'x'.

As per question, three quarters are white. So,

Number of white boats (w) = $\frac{3}{4}\times x=\frac{3x}{4}$

Now, boats remaining are given as:

Remaining boats = Total boats - White boats

Remaining boats = $x-\frac{3x}{4}=\frac{4x}{4}-\frac{3x}{4}=\frac{4x-3x}{4}=\frac{x}{4}$

As per question, 4/7 of the remaining boats are blue.

Number of blue boats (b) = $\frac{4}{7}\times \frac{x}{4}=\frac{x}{7}$

Now, the rest are red. So,

Number of red boats (r) = Total number - ( White boats + Blue boats )

$r=x-(w+b)$

Plug in 9 for 'r', $\frac{3x}{4}$ for 'w' and $\frac{x}{7}$ for 'b'. Solve for 'x'. This gives,

$9=x-(\frac{3x}{4}+\frac{x}{7})\\\\9=x-(\frac{3x\times 7}{4\times 7}+\frac{x\times 4}{7\times 4})\\\\9=x-(\frac{21x}{28}+\frac{4x}{28})\\\\9=x-\frac{21x+4x}{28}\\\\9=\frac{28x}{28}-\frac{25x}{28}\\\\9=\frac{28x-25x}{28}\\\\9\times 28=3x\\\\x=\frac{9\times 28}{3}=3\times 28=84$

Therefore, the total number of boats in the marina are 84.