Arthur D. answered • 06/28/15
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Here's another solution. I think the amount of each solution is missing.
7:3 means 7/10=70% milk
3:2 means 3/5=60% milk
assume each solution is 100 liters
70%(x)+60%(100-x)=66 2/3%(100) because 2:1 means 2/3=66 2/3 % milk
0.7x+0.6(100-x)=66 2/3
0.7x+60-0.6x=66 2/3
0.1x+60=66 2/3
0.1x=6 2/3
x=66 2/3
100-x=33 2/3
66 2/3 of the 70% mixture and 33 2/3 of the 60% mixture
check: (2/3)(70)+(1/3)(60)=(2/3)(100)
46 2/3+20=66 2/3
66 2/3=66 2/3
Denise C.
I don't think you need an absolute amount for this particular problem although I think you can assume the amount in vessel A is the same as the amount in vessel B. Ratios involve relative amounts like 1 part from vessel A to 5 parts in vessel B to yield a mixture of 2 parts milk and 1 part water, 2:1.
Also, i'm not sure about the statement in the very beginning. "Because 2:1 means 2/3..." 2:1 means 2/1 and 2/1 does not equal 2/3 therefore you can't substitute one with the other.
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06/30/15
Arthur D.
tutor
Denise, if the ratio is 2:1, this means 2 parts milk and 1 part water. Therefore, there are 3 parts altogether, 2 parts milk and 1 part water. So the amount of milk is 2/3 of the entire amount. If you had 6 red marbles and 4 blue marbles the ratio of red to blue would be 6/4 or 3/2 and the total number of marbles would be 6+4=10. There would be 6 red out of 10 marbles. And, yes, the ratio 2:1 does mean 2 parts out of 3 parts, or 2/3. If the ratio of boys to girls in a school is 2:1 this means for every 2 boys there is 1 girl. If there are 4 boys, then there are 2 girls for a total of 6 students, and 4 boys out of 6 students is 4 out of 6 or 4/6=2/3 of the students are boys.
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07/01/15
Denise C.
The problem is: "...find the ratio in which the quantity be taken from the vessels ..." or x parts from vessel A to y parts from vessel B will yield a solution of 2 parts milk to 1 part water.
2 parts milk : 1 part water is different than saying 2/3 milk or 1/3 water. Of course there's a relationship between them all, but they state different things. After all, are you really saying, 2/1 = 2/3 ? Hope not.
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07/01/15
Arthur D.
tutor
Denise, I'm saying that 2 parts milk and 1 part water "means" 2/3 of the solution is milk. The ratio of milk to the entire solution is 2:3. Why don't you get a second opinion from someone and then you'll see that the ratio of milk to water, which is 2:1, means that 2/3 of the mixture is milk.
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07/02/15
Arthur D.
tutor
Denise, Why don't you google ratio 2:1 and see what it says and then maybe you'll be convinced that what I say is true.
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07/02/15
Denise C.
Hi Arthur,
I think you missed my point. I don't disagree with the fact that a ratio or 2(milk):1(water) is the same as 66.666% milk and 33.3333% water.
I believe the question is asking to "find the RATIO in which the quantity be taken from the vessels so that the ratio of milk and water in the new mixture is 2:1". Although I must say, there seems to be a grammatical error or two if you careful re-read from above. Anyways, I was solving for the question here highlighted in bold.
I believe the problem is asking for the ratio of vessel A to vessel B (A:B) to yield a final mixture of 2 parts milk to 1 part water (2:1). The ratio 2:1 is given. We're solving for A:B.
You would prefer to interpret the given (2:1) as percentage of milk 66.666%, not percentage of water and not parts milk to parts water, as requested. Okay not a huge deviation but a difference where you're expressing the percentage of one component versus the ratio. After all, if you were looking for the percentage of water or even the ratio of water:milk (the inverse of milk:water), you would get a different answer.
Here's the concern I have. You're taking the given part of the problem (2 milk:1 water), interpreting it as the percentage of milk 66.666% or as you have stated 66 2/3 and calling it the solution. It's not the solution, it's the given part of the problem.
They are asking what is the ratio of vessel A to vessel B to provide, as you would say, 66 2/3% milk, 33 1/3% water in the final mixture. What is the ratio of A:B? Does the ratio (A:B) ) equal 66 2/3? no. Does the percentage of vessel A = 66 2/3%? no. Does the percentage of vessel B = 66 2/3%? no. They did not ask, What is the percentage of milk in the final mixture? Had that been the question, your answer would be correct.
And on a last note, Arthur you seem like a nice guy. But I'm ready to move on. I guess we just disagree. Take care.
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07/02/15
Arthur D.
tutor
Denise, I agree that we disagree but at least we agree to move on to the next problem. It was fun and challenging to go back and forth with our arguments. I really think that the problem was poorly worded. Anyway, you seem nice too.
Have a good day.
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07/03/15
Denise C.
06/28/15