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Box1 contains 500 marbles, 24% of which are black.Box2 contains some marbles of which 10% are black.You put the marbles together in another box and found that the percentage of black marble is 20%. How many medals were there in box 2?
A. 100
B.150
C. 200
D. 250
E. None of these

Respuesta :

LammettHash

Let [tex]b_1[/tex] and [tex]b_2[/tex] denote the number of black marbles in box 1 and 2, respectively, and [tex]n_1[/tex] and [tex]n_2[/tex] the total number of marbles in box 1 and 2, respectively. Then

[tex]\dfrac{b_1}{n_1}=\dfrac{b_1}{500}=24\%\implies b_1=120[/tex]

[tex]\dfrac{b_2}{n_2}=10\%\implies10b_2=n_2[/tex]

[tex]\dfrac{b_1+b_2}{n_1+n_2}=\dfrac{120+b_2}{500+n_2}=20\%\implies10(120+b_2)=2(500+n_2)[/tex]

[tex]\implies600+5b_2=500+n_2[/tex]

[tex]\implies5b_2=n_2-100[/tex]

Since [tex]b_2=\dfrac{n_2}{10}[/tex], we have

[tex]\dfrac{5n_2}{10}=n_2-100\implies1000=5n_2\implies n_2=200[/tex]

so there were 200 marbles in total in box 2 at the start.

There are 200 marbles were there in box2.

Given that,

Box1 contains 500 marbles, 24% of which are black.

Box2 contains some marbles of which 10% are black.

You put the marbles together in another box and found that the percentage of black marble is 20%.

We have to determine,

How many marbles were there in box 2?

According to the question,

Let, [tex]B_1[/tex] denote the number of black marbles in box1,

and [tex]B_2[/tex] denote the number of black marbles in box2, respectively.

Then,

The total number of marbles in box1 is,

[tex]= \dfrac{b_1}{n_1} = 0.24\\\\= \dfrac{b1}{500} = 0.24\\\\= b_1 = 120[/tex]

And, The total number of marbles in box2 is,

[tex]= \dfrac{b_2}{n_2} = 0.10\\\\= b_2 = 0.10 \ \times n_2[/tex]

The marbles together in another box and found that the percentage of black marble is 20%.

[tex]=\dfrac{b_1+b_2}{n_1+n_2} = 0.20\\\\= \dfrac{120+b_2}{500+n_2} = 0.20\\\\= 120 + b_2 = 0.20 (500 + n_2) \\\\= 120 + b_ 2 = 100 + 0.20 \ n_2[/tex]

Substitute the value of [tex]b_2 = 0.10 \times n_2[/tex] in the given equation,

[tex]120 + b_2 = 100 + 0.20\ n_2\\\\120 + 0.10 \ n_2 = 100 + 0.20 \ n_2\\\\120 - 100 = 0.20 \ n_2 - 0.10 \ n_2\\\\20 = 0.10 \ n_2 \\\\n _2 = \dfrac{20}{0.10}\\\\n_ 2= 200[/tex]

Hence, there are 200 marbles were there in box2.

To know more about Probability click the link given below.

https://brainly.com/question/21586810

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