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

Show answers

Answers

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 :

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

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

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

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

Learn more

5 - 1 1/4 will be more than 4

link

spend practicing instruments

link

spend on the comic books

link

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

m∠a is 90°

m∠b is 40°

Need finding and figuring out for angle a & b:

Answer from: Quest

X= -5because this is a single step equation so you would just have to divide -16 both sides for x to equal your solution

Another question on Mathematics

Mathematics, 21.06.2019 16:20

Match each statement with its corresponding value for the system below: y = -2(3)x and y = 9x - 2 1. the number of points of intersection. -2 2. the x-coordinate of the solution. 1 3. the y-coordinate of the solution. 0

Answers: 3

Answer

Mathematics, 21.06.2019 16:30

An equation where variables are used to represent known values—function notation true or false

Answers: 2

Answer

Mathematics, 21.06.2019 17:30

Select the quadratic that has root x = 8 and x = -5

Answers: 3

Answer

Mathematics, 21.06.2019 21:30

Ok a point t on a segment with endpoints d(1, 4) and f(7, 1) partitions the segment in a 2: 1 ratio. find t. you must show all work to receive credit.

Answers: 1

Answer

You know the right answer?

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

Questions