Work backwards from the file cost. The file ($4) is 1/2 of the remainder after food; that remainder is 2/3 of the total.
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• File = $4 = 1/2 of remainder after food
• Remainder after food → $4 × 2 = $8
• Remainder = 2/3 of total → 1/3 = $8 ÷ 2 = $4
• Total at first → $4 × 3 = $12
Mindy had $12 at first.
Check: Food = 1/3 × $12 = $4. Remainder = $8. File = 1/2 × $8 = $4. Left = $4. Total = $4 + $4 + $4 = $12. ✓