Mathematics, 10.11.2019 01:31 tressasill

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?

Answers: 3

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Answer from: 10040813

Step-by-step explanation:

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

Then, The number of white boats= $\frac{3}{4}x$

then the remaining boats= $x-\frac{3x}{4}=\frac{x}{4}$

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

Thus, the number of blue boats= $\frac{4}{7}\times\frac{x}{4}=\frac{x}{7}$

The rest of the boats (red boats)= $\frac{x}{4}-\frac{x}{7}=\frac{7x-4x}{28}=\frac{3x}{28}$

The number of red boats=9

Thus,

$\frac{3x}{28}=9\\\Rightarrow\ x=\frac{28\times9}{3}\\\Rightarrow\ x=84$

The total number of boats in the marine = 84

Answer from: samone26

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

$\large{\boxed{\bold{\frac{a}{b}} }$

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

$\displaystyle white~boat=\boxed{\frac{3}{4}x}$

$\frac{4}{7}$ of the remaining boats are blue

$\displaystyle remaining~boat=x~-\frac{3}{4}x=\frac{1}{4}x$

$\displaystyle blue~boat=\frac{4}{7}\times\frac{1}{4}x=\frac{4}{28}x=\frac{1}{7}x$

total boats

$\displaystyle total~boats=x=\frac{3}{4}x+\frac{1}{7}x+9$

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 :

$\displaystyle \frac{21}{28}x+\frac{4}{28}x+9=x$

$\displaystyle \frac{25}{28}x+9=x$

$\displaystyle \frac{3}{28}x=9$

$\large{\boxed{\boxed{\bold{x=84}}}$

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Keywords : boats, marina, fractions

Three quarters of the boats in the marina are white. 4/7 of the remaining boats are blue, and the re

Answer from: Quest

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.

Answer from: Quest

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

$x^2-2x+y^2-6y=26$

we now create space between the x and y terms with parenthesis.

$(x^2-2x)+(y^2-6y)=26$

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

$\frac{-2}{2} =(-1)^{2} =1$

$\frac{-6}{2} =(-3)^{2} =9$

we add the squares to both sides.

$(x^2-2x+1)+(y^2-6y+9)=26+1+9$

simplify.

$(x^2-2x+1)+(y^2-6y+9)=36$

and write the quadratics in factored form.

$(x-1)^{2} +(y-3)^{2} =36$

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

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