A box contains red, blue and green marbles in the ratio 2 : 3 : 5. After 12 red marbles are added and 6 blue marbles are removed, the ratio becomes 4 : 3 : 5. Find the original total number of marbles.
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Worked Solution
Step 1: Let original red = 2u, blue = 3u, green = 5u.
Step 2: After change: red = 2u + 12, blue = 3u − 6, green = 5u (unchanged).
Step 3: New ratio (2u + 12) : (3u − 6) : 5u = 4 : 3 : 5.
Step 4: Compare green ratios: 5u corresponds to 5 in new ratio, so unit is preserved. From red: 2u + 12 = 4u → u = 6.
Step 5: Original total = 10u = 60.
Answer: 60
Correct answer: 60
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