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.

Question

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

Answer 1

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.