Mathematics, 25.06.2019 20:00 napoleonbrown

Of 560 marbles in a bag, 65% are red and the rest are blue. after 28 red marbles are replaced with blue ones, how many blue marbles need to be added to the bag so that the 65% of all marbles are blue?

Answers: 2

Show answers

Answers

Answer from: epunisa

The answer is 400 blue marbles.

Step-by-step explanation: Given that there are 560 marbles in a bag, out of which 65% are red and rest are blue.

So, number of red marbles is

$n_r=65\%\times 560=\dfrac{65}{100}\times 560=364,$

and number of blue marbles is

n_b=560-364=196.

Now, if 28 red marbles are replaced by blue marbles, the the new number of red and blue marbles will be

$n_r^\prime=364-28=336~~~\textup{and}~~~n_b^\prime=196+28=224.$

Now, to get 65% of the marbles blue, we need to add some more blue marbles to the bag. Let 'x' number of blue marbles are added to the bag, then

$65\%\times (560+x)=224+x\\\\\Rightarrow \dfrac{65}{100}\times (560+x)=224+x\\\\\Rightarrow 13(560+x)=20(224+x)\\\\\Rightarrow 7280+13x=4480+20x\\\\\Rightarrow 7x=2800\\\\\Rightarrow x=400.$

Thus, 400 blue marbles need to be added to the bag.

Answer from: queen6931

$\boxed{{\mathbf{400}}}$ marbles are needed to add in the bag to maintain $65\%$ of all marbles are blue.

Further explanation:

Given

There are total 560 marbles in bag in which $65\%$ are red and the rest are blue. It has been found that 28 red marbles has been replaced by blue marbles.

Step by step explanation:

Step 1:

It is given that $65\%$ are red marbles and the total number of marbles are 560.

The total number of red marbles initially can be calculated as,

$\begin{aligned}{\text{number of red marbles}} &= \frac{{65}}{{100}} \times 560 = 0.65 \times 560\\&= 364\\\end{aligned}$

Therefore, the total number of red marbles initially are 364.

Step 2:

It is given that rest of the marbles are blue that means $35\%$ of the total marbles.

The total number of blue marbles can be evaluated as,

$\begin{aligned}{\text{number of blue marbles}} &= 560 - 364\\&= 196 \\\end{aligned}$

Therefore, the total number of blue marbles initially are 364.

Step 3:

Now it is given that the 28 red marbles are replaced with blue marbles.

Now red marbles after the replacement can be evaluated as,

$\begin{aligned}{\text{number of red marbles}} &= 364 - 28\\&= 336\\\end{aligned}$

Now blue marbles after the replacement can be calculated as,

$\begin{aligned}{\text{number of blue marbles}} &= 196 + 28 \\&= 224 \\\end{aligned}$

Therefore, the number of red marbles are 336 and the number of blue marbles are 224.

Step 4:

Now find the number of blue marbles added in the bag to maintain $65\%$ blue marbles.

Consider as the number of blue marbled added in the bag so that $65\%$ of all marbles are blue.

Now determine an equation for the percent of blue marbles.

$\begin{aligned}\left( {\frac{{224 + x}}{{560 + x}}} \right) \times 100 &= 65 \\ \frac{{224 + x}}{{560 + x}} &= \frac{{65}}{{100}} \\\end{aligned}$

Step 5:

Now cross multiply the resultant equation and use the distributive property to obtain the value of .

$\begin{aligned}\left( {224 + x} \right)100 &= 65\left( {560 + x} \right) \\22400 + 100x &= 36400 + 65x \\100x - 65x &= 36400 - 22400 \\35x &= 14000 \\\end{aligned}$

Further calculation for the value of can be calculated as,

$\begin{aligned}x&= \frac{{14000}}{{35}} \hfill \\x &= 400 \hfill \\\end{aligned}$

Therefore, 400 marbles are required to add in the bag so that $65\%$ of all marbles area blue.

Learn more:

Learn more about the solution of the linear equation Learn more about the problem of the linear equation Learn more about equations of the area and perimeter of the rectangle

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Permutation

Keywords: Blue marbles, red marbles, bag, cross multiply, added, replaced, total marbles, initially, replacement, distributive property, numbers

Answer from: Quest

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐

In the diagram of circle o, what is the measure of abc? 210 150

Answer from: Quest

idk man good luck man

Another question on Mathematics

Mathematics, 21.06.2019 16:30

The length of the largest fish is 967.74 times greater than the length of the smallest fish. select a variable expression that shows the length of the largest fish, if 8 is the length of the smallest fish. a. s + 967.74 b. \[ \frac{967.74}{s} \] c. 967.74 - s d. 967. 74s

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

Shannon drove for 540 minutes. if she traveled 65 miles per hour,how many total miles did she travel?

Answers: 2

Answer

Mathematics, 21.06.2019 23:00

What’s the volume of the triangular prism?

Answers: 2

Answer

Mathematics, 22.06.2019 00:00

An equation in slope-intersept form the lines that passes thought (-8,1) and is perpindicular to the y=2x-17.