A box contains some red and blue marbles. If Angeline adds in 10 red marbles, 60% of the marbles are blue. If she adds in 30 blue marbles, 75% of the marbles are blue. How many red marbles are there in the box?
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Question
Answer
Let number of blue & red marbles be B & R respectively.
First scenario:
Total number of Blue = B
Total number of Red = R + 10
Total number of marbles = B + R + 10
B / (B + R + 10) = 6/ 10 = 0.6
B = 0.6 (B + R + 10)
B = 0.6B + 0.6R + 6
0.4 B = 0.6R + 6
2B = 3R + 30 (both sides of equation x 5)
Second scenario:
Total number of Blue = B + 30
Total number of Red = R
Total number of marbles = B + R + 30
(B + 30) / (B + R + 30) = 75/100 = 0.75
B + 30 = 0.75 (B + R + 30)
B + 30 = 0.75B + 0.75R + 22.5
0.25B = 0.75R – 7.5
2B = 6R – 60 (both sides of equation x 8)
Therefore:
2B = 3R + 30 = 6R -60
3R = 90
R = 30
Let number of blue & red marbles be B & R respectively.
First scenario:
Total number of Blue = B
Total number of Red = R + 10
Total number of marbles = B + R + 10
B / (B + R + 10) = 6/ 10 = 0.6
B = 0.6 (B + R + 10)
B = 0.6B + 0.6R + 6
0.4 B = 0.6R + 6
2B = 3R + 30 (both sides of equation x 5)
Second scenario:
Total number of Blue = B + 30
Total number of Red = R
Total number of marbles = B + R + 30
(B + 30) / (B + R + 30) = 75/100 = 0.75
B + 30 = 0.75 (B + R + 30)
B + 30 = 0.75B + 0.75R + 22.5
0.25B = 0.75R – 7.5
2B = 6R – 60 (both sides of equation x 8)
Therefore:
2B = 3R + 30 = 6R -60
3R = 90
R = 30