mighty1399
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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?

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JeanaShupp

Answer: 84


Step-by-step explanation:

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

Then, The number of white boats= [tex]\frac{3}{4}x[/tex]

then the remaining boats= [tex]x-\frac{3x}{4}=\frac{x}{4}[/tex]

Now, 4/7 of the remaining boats are blue.

Thus, the number of blue boats=[tex]\frac{4}{7}\times\frac{x}{4}=\frac{x}{7}[/tex]

The rest of the boats (red boats)=[tex]\frac{x}{4}-\frac{x}{7}=\frac{7x-4x}{28}=\frac{3x}{28}[/tex]

The number of red boats=9

Thus,

[tex]\frac{3x}{28}=9\\\Rightarrow\ x=\frac{28\times9}{3}\\\Rightarrow\ x=84[/tex]

The total number of boats in the marine = 84


ardni313

There are 84 boats in the marina

Further explanation  

Fraction numbers are known as numerator and denominator  

On a number line, fractions are expressed in points that lie between two integers  

The general form of fractions is  

[tex]\large{\boxed{\bold{\frac{a}{b}} }[/tex]  

a = numerator  

b = denominator  

Mixed fractions consist of whole number and proper fractions  

There are a number of steps in adding fraction operations  

  • 1. the denominators must be the same, if not then

a. Multiply top and bottom of each fraction by the denominator of the other. or  

b. we can use Least Common Denominator which is the smallest of all the common denominators.  

  • 2. Add the numerators and put over the denominator  
  • 3. Simplify the fraction  

There are several steps to multiply fractions  

  • 1. Multiply the numerators  
  • 2. Multiply the denominators  
  • 3. Simplify the fraction  

  • Three quarters of the boats in the marina are white

we translate this sentence into equation:  

Let x = total boats

[tex]\displaystyle white~boat=\boxed{\frac{3}{4}x}[/tex]

  • [tex]\frac{4}{7}[/tex]  of the remaining boats are blue

[tex]\displaystyle remaining~boat=x~-\frac{3}{4}x=\frac{1}{4}x[/tex]

[tex]\displaystyle blue~boat=\frac{4}{7}\times\frac{1}{4}x=\frac{4}{28}x=\frac{1}{7}x[/tex]

  • total boats

[tex]\displaystyle total~boats=x=\frac{3}{4}x+\frac{1}{7}x+9[/tex]

Because the denominator is not the same, so we can use both multiplying or least common denominator.  

let we use least common denominator:  

List multiples of 7: 7, 14, 21,28,...

List multiples of 4: 4, 8, 12, 16, 20,24,28, ...  

the smallest number that is the same: = 28

then addition operation becomes :  

[tex]\displaystyle \frac{21}{28}x+\frac{4}{28}x+9=x[/tex]

[tex]\displaystyle \frac{25}{28}x+9=x[/tex]

[tex]\displaystyle \frac{3}{28}x=9[/tex]

[tex]\large{\boxed{\boxed{\bold{x=84}}}[/tex]

Learn more  

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Keywords : boats, marina, fractions

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