Question 810229: A bag contains 7 red marbles and 5 black marbles. You must add 60 marbles to the bag, but the ratio of red to black must remain the same. How many of each color should you add?
Found 2 solutions by TimothyLamb, DrBeeee:
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! 7/5 = r/b
r + b = 12
R + B = 60
R = 60 - B
(R+7)/(B+5) = 7/5
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(R+7)/(B+5) = 7/5
(60 - B + 7)/(B + 5) = 7/5
(67 - B)/(B + 5) = 7/5
67 - B = (7/5)(B + 5)
67 - B = (7/5)B + 7
60 = (7/5)B + (5/5)B
60 = (12/5)B
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B = 25
R = 35
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Answer by DrBeeee(684)  (Show Source):
You can put this solution on YOUR website! You have 7 red marbles and 5 black marbles for a total number of 12 marbles, right? When you add 60, you have a new total of 72, correct? To keep the same ratio of red/total, we have the proportion
(1) 7/12 = red/72 or
(2) red = 72*7/12 or
(3) red = 42
That is, you will have 42 total red marble and
(4) black = 72 - 42 = 30 or we have a total of 30 black marbles
The ratio of red to black is
(6) 42/30 = 7/5, the same as before we added 60 marbles.
Answer: We should add 35 red marbles and 25 black marbles (total of 60 marbles).
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