Question

There are white, blue, and red boats in a marina. Five-sixths of the boats in the marina are white, 2/5 of the remaining boats are blue, and the rest are red. If there are 12 red boats, how many boats are in the marina?

Answer 1

Answer: There are 120 boats in marina.

Step-by-step explanation:

Let x be the total number of boats in the marina.

As per given , Number of white boats = $\dfrac{5}{6}x[\tex]

Number of blue boats = [tex]\dfrac{2}{5}(x-\dfrac{5}{6}x)=\dfrac{2}{5}(\dfrac{x}{6})=\dfrac{x}{15}[\tex]

Number of red boats = [tex]x-\dfrac{5}{6}x-\dfrac{x}{15}[\tex]

[tex]=x(\dfrac{30-25-2}{30})=x(\dfrac{3}{30})=\dfrac{x}{10}$

Since , Number of red boats = 12

Therefore, $\dfrac{x}{10}=12\Rightarrow\ x=12\times10=120$

Hence, there are 120 boats in marina.

Answer 2

There are 120 boats in the marine

Ratios and Proportion

Let the total boats in the marina be "x"

If five-sixths of the boats in the marina are white, 2/5 of the remaining boats are blue and the remaining are red, hence the fraction that are red is expressed as:

Fraction that are red = 1 - (5/6+1/15)

Fraction that are red = 1 - (25+2/30)

Fraction that are red = 1 - (27/30)

Fraction that are red =  3/30 = 1/10

Since there are 12 red boats, the total boat is calculated as:

1/10 of x = 12

x = 10 * 12

x = 120

Hence there are 120 boats in the marine

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