Ahmad has $a in his wallet. He spends 1/4 of his money on lunch at the hawker centre. Then he spends 2/5 of the REMAINING money on a book at Popular Bookshop. After both purchases, he has $36 left. Find the value of a.
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Worked Solution
Step 1: Let the original amount be $a. After spending 1/4 on lunch, the remainder is a − a/4 = 3a/4.
Step 2: Of this remainder, 2/5 is spent on the book, so 3/5 of the remainder is left. Money left after both purchases = 3a/4 × 3/5 = 9a/20.
Step 3: Set the money left equal to $36. 9a/20 = 36.
Step 4: Solve for a. a = 36 × 20 / 9 = 720 / 9 = 80.
Check: a = $80 → lunch = 80 × 1/4 = $20; remainder = $60; book = 60 × 2/5 = $24; left = 60 − 24 = $36 ✓.
Final answer: $80.
Answer: $80
Correct answer: $80
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