SOLUTION: 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?

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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