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Question 524232: a bag contains black, red and blue marbles in the ratio 3:5:2. if there are 35 red marbles in the bag, how many black marbles are in the bag?
could you please write out the steps on how to do it , i really dont understand, thankyou !
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let's just think about this problem and see if we can make some sense of it.
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The black marbles to red marbles to blue marbles must be in the ratio of 3 to 5 to 2. That means that the bag could have 3 black marbles if it also had 5 red marbles and 2 blue marbles.
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So the bag could have multiples of this ratio, and it would still be of the same ratio. In other words, the ratio would still be 3:5:2 if the bag contained 6 black marbles, 10 red marbles, and 4 blue marbles. (All we did is multiply the ratio by 2).
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Or the bag would still have the same ratio among marbles if it had 9 black marbles, 15 red marbles, and 6 blue marbles.
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Maybe you can now see where this is headed. The number of black marbles must be 3/5 the number of red marbles (from the ratio 3:5) and the number of blue marbles must be 2/5 of the number of red marbles (from the red to blue ratio of 5:2).
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So to have the same ratio between black and red we can set up a proportion:
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(3 black marbles)/(5 red marbles) = (Unknown black marbles)/(35 red marbles)
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Read that as "3 black marbles is to 5 red marbles as X is to 35 red marbles"
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In short form this becomes:
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You can get rid of the denominator on the right side by multiplying both sides by 35 to get:
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On the left side the 35 in the numerator can be divided by the 5 in the denominator to give a multiplier of 7. And on the right side the 35 in the denominator divides into (or cancels) the 35 in the numerator and the total result is:
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Multiplying this out we find that X, the unknown number or black marbles, is 21 when the number of red marbles is 35. These two numbers are in the ratio of 3:5. The number of black marbles (21) is 3/5 the number of red marbles (35).
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You weren't asked to do this next step, but for practice let's find out how many blue marbles are in the bag if there are 35 red marbles. From the last two numbers in the ration, 5:2, we know that for every 5 red marbles there are 2 blue marbles. (Or we could say that the number of blue marbles is 2/5 of the number of red marbles.) So we could multiply the number of red marbles (35) times 2/5 to find the number of blue marbles.
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And dividing 70 by 5 gives us the answer of 14. So when the number of red marbles is 35, we now know that the bag contains 21 black marbles and 14 blue marbles.
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Hope this helps you to understand what ratios of the form 3:5:2 mean and how, if you think about it, given one of the amounts you can figure out what the two other amounts would have to be. It just takes some thinking about this and a little practice, but it will eventually all make sense. Good luck.
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