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Grogg has two bags of marbles, each of which contains some red marbles and some blue marbles (and no marbles of any other color). The ratio of red marbles to blue marbles in the first bag is 3:5.The ratio of red marbles to blue marbles in the second bag is $3:2.$ When the two bags of marbles are mixed together, the ratio of red marbles to blue marbles is 11:9. What is the ratio of the number of marbles in the first bag to the number of marbles in the second bag?

 Jul 21, 2023
 #2
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Let b1​ and r1​ denote the number of blue and red marbles in the first bag, respectively, and let b2​ and r2​ denote the number of blue and red marbles in the second bag, respectively. Since the ratio of red marbles to blue marbles in the first bag is 3:5, r1​=83​b1​.

Similarly, r2​=53​b2​. When the two bags are mixed together, the total number of red and blue marbles is r1​+r2​ and b1​+b2​. Since the ratio of red marbles to blue marbles in the mixed bag is 11:9, we have [\frac{r_1 + r_2}{b_1 + b_2} = \frac{11}{9}.]Substituting in our expressions for r1​ and r2​, we get [\frac{\frac{3}{8} b_1 + \frac{3}{5} b_2} {b_1 + b_2} = \frac{11}{9}.]Multiplying both sides by 8b1​+5b2​ and simplifying, we get [9b_1 + 11b_2 = 44b_1 + 33b_2.]Solving for b1​/b2​, we find [\frac{b_1}{b_2} = \boxed{6:5}.]

 Jul 21, 2023
 #12
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what does  \boxed{6:5}.] mean

Guest Jul 23, 2023
 #13
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It means 6:5 obviously. 

HumenBeing  Jul 23, 2023
 #7
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Although some of you slightly overreacted, I agree that no one should post questions that are from BA, especially one that is so obviously from your homework. But answering them will harm the cheater more than anyone else. All in all, I do NOT encourage cheating, as it harms you more than anyone else, even the people putting in the time to correctly answer.

 Jul 22, 2023
 #11
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And it isn't fair. A lot of posts about cheating have no "real" evidence, but this question is from Beast Acadamy 100%, you can tell because the name Grogg is one of the little monsters. I saw questions like this when I was doing BA problems

HumenBeing  Jul 22, 2023
edited by HumenBeing  Jul 22, 2023

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