Let the cost of a pie be 1 part. A cake costs 1 part + $2.50.
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• 9 cakes + 13 pies = 9(1 part + $2.50) + 13(1 part)
• = 22 parts + (9 × $2.50) = 22 parts + $22.50
• 22 parts + $22.50 = $72
• 22 parts = $72 - $22.50 = $49.50
• 1 part = $49.50 ÷ 22 = $2.25 (cost of a pie)
• Cost of a cake = $2.25 + $2.50 = $4.75
The cost of each cake is $4.75.
Check: 9 × 4.75 + 13 × 2.25 = 42.75 + 29.25 = 72. ✓