Mike bought 17 bottles of beer from a shop. He wants to move these bottles to his car. If he can only carry 3 bottles at a time, what is the minimum number of trips he needs to make to carry these bottles? Answer: 6.
The correct answer and explanation is:
Answer: Mike needs to make 6 trips to carry all 17 bottles.
Explanation:
Mike has 17 bottles to carry, but he can only carry 3 bottles per trip. To find out how many trips he needs to make, we divide the total number of bottles by the number of bottles he can carry each trip: Number of trips=173\text{Number of trips} = \frac{17}{3}
Doing the division: 17÷3=5 remainder 217 \div 3 = 5 \text{ remainder } 2
This means that if Mike makes 5 trips carrying 3 bottles each, he will have carried: 5×3=15 bottles5 \times 3 = 15 \text{ bottles}
But since he has 17 bottles in total, there are still 2 bottles left after those 5 trips. Therefore, he will need one more trip to carry these remaining 2 bottles.
So the total number of trips required is: 5+1=6 trips5 + 1 = 6 \text{ trips}
Why can’t it be fewer trips?
Even though Mike can carry 3 bottles per trip, the total number (17) is not divisible evenly by 3. If he tries to carry 3 bottles for 5 trips, he carries only 15 bottles, leaving 2 bottles behind. Since he can’t carry more than 3 bottles in a trip, he must take a sixth trip to carry the remaining 2 bottles.
Generalizing the approach:
For any number of items nn and a maximum carry capacity per trip cc:
- Divide nn by cc.
- The quotient tells you how many full trips carrying cc items you can make.
- The remainder tells you if an additional trip is needed (if remainder > 0, add 1 trip).
This method ensures you find the minimum number of trips required when you have a fixed carrying capacity.
Summary:
- Mike has 17 bottles.
- He can carry 3 bottles per trip.
- 17 divided by 3 is 5 full trips plus 2 bottles left.
- Therefore, 6 trips total are needed.
This ensures Mike moves all bottles in the fewest trips possible without exceeding his carrying limit.