Ahmad has two bags of marbles. Bag A : Bag B = 5 : 3. If Ahmad moves 8 marbles from Bag A to Bag B, the new ratio of Bag A to Bag B is 9 : 7. Find the total number of marbles.
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Worked Solution
Step 1: Let Bag A = 5k and Bag B = 3k (original ratio 5:3).
Step 2: After moving 8 marbles: Bag A = 5k − 8, Bag B = 3k + 8.
Step 3: New ratio: (5k − 8) / (3k + 8) = 9 / 7.
Step 4: Cross-multiply: 7(5k − 8) = 9(3k + 8) → 35k − 56 = 27k + 72 → 8k = 128 → k = 16.
Step 5: Total = 5k + 3k = 8k = 8 × 16 = 128 marbles.
Correct answer: 128
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