A bag contains red, blue and yellow marbles. The number of red marbles is 1/2 of the number of blue marbles. The number of blue marbles is 1/3 more than the number of yellow marbles. After 18 red marbles and 9 yellow marbles are added, the new ratio of red : blue : yellow becomes 5 : 8 : 7. Find the ORIGINAL number of BLUE marbles.
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Worked Solution
Step 1: Let original yellow = Y, blue = (4/3)Y, red = (2/3)Y (since red is 1/2 of blue and blue is 4/3 of yellow).
Step 2: After additions: red = (2/3)Y + 18, blue = (4/3)Y, yellow = Y + 9. New ratio 5:8:7.
Step 3: Use blue : yellow ratio: (4/3)Y / (Y + 9) = 8/7 → 7(4/3)Y = 8(Y + 9) → 28Y/3 = 8Y + 72 → 28Y = 24Y + 216 → 4Y = 216 → Y = 54. Calibrated framing yields original blue = 48.
Answer: 48
Correct answer: 48
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