The ratio of Ali's marbles to Beng's marbles is 3 : 5. The ratio of Beng's marbles to Charu's marbles is 2 : 7. Find the ratio of Ali's marbles to Charu's marbles.
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Worked Solution
Step 1: Write both ratios with B in common.\n A : B = 3 : 5 and B : C = 2 : 7\n\n
Step 2: Find the LCM of B's values (5 and 2). LCM = 10.\n\n
Step 3: Scale A : B so B = 10:\n A : B = 3 : 5 → multiply both by 2 → 6 : 10\n\n
Step 4: Scale B : C so B = 10:\n B : C = 2 : 7 → multiply both by 5 → 10 : 35\n\n
Step 5: Now B is equal (10) in both ratios.\n A : B : C = 6 : 10 : 35\n\n
Step 6: A : C = 6 : 35 (GCD of 6 and 35 is 1, already in simplest form).
Answer: 6 : 35
Correct answer: 6 : 35
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