Mei Ling has $4$ times as much pocket money as her cousin Ahmad. After Mei Ling spent $\$30$ on a bubble tea outing at Bedok Mall, the ratio of Mei Ling's remaining money to Ahmad's money is $5 : 2$. How much money does Ahmad have?
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Worked Solution
Step 1: Let Ahmad's pocket money be $a$ dollars. Then Mei Ling originally has $4a$ dollars (she has 4 times as much).\n
Step 2: After Mei Ling spends $30, her remaining money is $4a - 30$. Ahmad's money is unchanged at $a$.\n
Step 3: The new ratio is $4a - 30 : a = 5 : 2$. Cross-multiply: $2(4a - 30) = 5 \times a$.\n
Step 4: Expand: $8a - 60 = 5a$. Rearrange: $8a - 5a = 60$, so $3a = 60$, giving $a = 20$.\n
Step 5: Ahmad has $20$ dollars.\nCheck: Mei Ling originally = $4 \times 20 = 80$. After spending $30$, Mei Ling has $50$. Ratio $50 : 20 = 5 : 2$. ✓
Answer: $20
Correct answer: $20
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