Aisha and Bala collect stamps in the ratio $A : B = 3 : 5$. After Aisha buys $6$ more stamps, the new ratio becomes $A : B = 9 : 10$. How many stamps did Bala have ORIGINALLY?
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Worked Solution
Step 1: Use the original ratio to introduce a unit. Let Aisha = $3k$ and Bala = $5k$. Bala's count does NOT change in this problem.\n
Step 2: After Aisha buys $6$ more stamps, Aisha = $3k + 6$ and Bala is still $5k$. The new ratio gives $(3k + 6) : 5k = 9 : 10$.\n
Step 3: Cross-multiply: $10(3k + 6) = 9 \\times 5k$, so $30k + 60 = 45k$.\n
Step 4: $45k - 30k = 60 \\Rightarrow 15k = 60 \\Rightarrow k = 4$.\n
Step 5: Bala originally = $5k = 5 \\times 4 = 20$ stamps.\nCheck: Aisha originally $3 \\times 4 = 12$; after gaining $6$, Aisha = $18$. New ratio $18 : 20 = 9 : 10$. ✓
Answer: 20
Correct answer: 20
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