Bridget bakes 48 loaves of bread for her bakery. She sells half of them in the morning for each. In the afternoon she sells two thirds of what she has left, and because they are not fresh, she charges only half price. In the late afternoon she sells the remaining loaves at a dollar each. Each loaf costs for her to make. In dollars, what is her profit for the day?
- A)
- B)
- C)
- D)
- E)
Answer
E
Key insight
Track the loaves in three batches (24, 16, 8) with prices 2.50, 1.25, 1.00 to get revenue 88, then subtract the cost 48 times 0.75 = 36.
Solution
Follow the loaves through the day.
- Morning: half of is loaves at , earning .
- Afternoon: loaves remain; two thirds of them is loaves at half price, , earning .
- Late afternoon: the last loaves at each earn .
Total revenue: .
Every loaf cost to make, so the total cost is .
Profit . The answer is .
Why this works
Multi-stage selling problems are bookkeeping: at each stage record how many items are left and the price, and keep a running revenue. The only conceptual step is that profit means revenue minus the cost of everything produced, not just the items sold at full price.
The trap
Reporting the revenue (88) or forgetting the cost of all 48 loaves, or taking two thirds of 48 instead of two thirds of the 24 loaves left.
Common mistakes
- Reporting the revenue (88) or forgetting the cost of all 48 loaves, or taking two thirds of 48 instead of two thirds of the 24 loaves left.
- Charging half of as or using the full price in the afternoon, which shifts the revenue to a different choice.
Techniques
Set up the equation/formula and compute; no special trick needed