Hakim has $2 notes and $5 notes. The ratio of the number of $2 notes to $5 notes is 4 : 1. He has $260 in total. He exchanges all his $2 notes for $5 notes (getting as many whole $5 notes as possible). How many $5 notes does he have in the end?
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Worked Solution
Step 1: Let $5 notes = k and $2 notes = 4k (ratio 4:1).
Step 2: Total value: 2(4k) + 5k = 8k + 5k = 13k = $260 → k = 20.
Step 3: $2 notes = 4k = 80 notes. $5 notes = k = 20 notes.
Step 4: Value of $2 notes = 80 × $2 = $160.
Step 5: New $5 notes from exchange = $160 ÷ $5 = 32 notes.
Step 6: Total $5 notes = original 20 + new 32 = 52 notes.
Correct answer: 52
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