Question
Barry’s Bagel Emporium sells a dozen bagels for $5.00. This price is no longer high enough to create a profit. The owner decides to raise the price. He does not want to alarm his customers with too large of an increase. He is considering four different plans.
Plan A: Raise the price by $0.05 each week until the price reaches $8.00.
Plan B: Raise the price by 10 percent each week until the price reaches $8.00.
Plan C: Raise the price by the same amount each week for 6 weeks, so that in the sixth week the price is $8.00.
Plan D: Raise the price by $0.25 each week until the price reaches $8.00.
Which plan will result in the price of the bagels reaching $8.00 fastest?
plan A
plan B
plan C
plan D
Mark this and return
Plan A: Raise the price by $0.05 each week until the price reaches $8.00.
Plan B: Raise the price by 10 percent each week until the price reaches $8.00.
Plan C: Raise the price by the same amount each week for 6 weeks, so that in the sixth week the price is $8.00.
Plan D: Raise the price by $0.25 each week until the price reaches $8.00.
Which plan will result in the price of the bagels reaching $8.00 fastest?
plan A
plan B
plan C
plan D
Mark this and return
Answers
GPT-4o mini
To determine which plan will result in the price of the bagels reaching $8.00 the fastest, we can calculate the price after each week for each plan:
1. **Current price of a dozen bagels = $5.00**
2. **Plan A**: Raise the price by $0.05 each week until it reaches $8.00.
- Increases by $0.05 each week.
- Increase needed to reach $8.00: $8.00 - $5.00 = $3.00.
- Weeks to reach $8.00: $3.00 / $0.05 = 60 weeks.
3. **Plan B**: Raise the price by 10 percent each week until it reaches $8.00.
- Week 1: $5.00 * 1.10 = $5.50
- Week 2: $5.50 * 1.10 = $6.05
- Week 3: $6.05 * 1.10 = $6.655
- Week 4: $6.655 * 1.10 ≈ $7.3205
- Week 5: $7.3205 * 1.10 ≈ $8.05255 (reaches $8.00 in week 5).
- Weeks to reach $8.00: 5 weeks.
4. **Plan C**: Raise the price by the same amount each week for 6 weeks so that in the sixth week the price is $8.00.
- Increase needed over 6 weeks: $8.00 - $5.00 = $3.00.
- Amount to raise each week: $3.00 / 6 = $0.50.
- Weeks to reach $8.00: 6 weeks.
5. **Plan D**: Raise the price by $0.25 each week until it reaches $8.00.
- Increase needed to reach $8.00: $3.00.
- Weeks to reach $8.00: $3.00 / $0.25 = 12 weeks.
Now, summarizing the weeks:
- Plan A: 60 weeks
- Plan B: 5 weeks
- Plan C: 6 weeks
- Plan D: 12 weeks
**Conclusion:** Plan B will result in the price of the bagels reaching $8.00 the fastest, in just 5 weeks.
1. **Current price of a dozen bagels = $5.00**
2. **Plan A**: Raise the price by $0.05 each week until it reaches $8.00.
- Increases by $0.05 each week.
- Increase needed to reach $8.00: $8.00 - $5.00 = $3.00.
- Weeks to reach $8.00: $3.00 / $0.05 = 60 weeks.
3. **Plan B**: Raise the price by 10 percent each week until it reaches $8.00.
- Week 1: $5.00 * 1.10 = $5.50
- Week 2: $5.50 * 1.10 = $6.05
- Week 3: $6.05 * 1.10 = $6.655
- Week 4: $6.655 * 1.10 ≈ $7.3205
- Week 5: $7.3205 * 1.10 ≈ $8.05255 (reaches $8.00 in week 5).
- Weeks to reach $8.00: 5 weeks.
4. **Plan C**: Raise the price by the same amount each week for 6 weeks so that in the sixth week the price is $8.00.
- Increase needed over 6 weeks: $8.00 - $5.00 = $3.00.
- Amount to raise each week: $3.00 / 6 = $0.50.
- Weeks to reach $8.00: 6 weeks.
5. **Plan D**: Raise the price by $0.25 each week until it reaches $8.00.
- Increase needed to reach $8.00: $3.00.
- Weeks to reach $8.00: $3.00 / $0.25 = 12 weeks.
Now, summarizing the weeks:
- Plan A: 60 weeks
- Plan B: 5 weeks
- Plan C: 6 weeks
- Plan D: 12 weeks
**Conclusion:** Plan B will result in the price of the bagels reaching $8.00 the fastest, in just 5 weeks.