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27 Nov 2020, 07:37
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Highest: 120
Lowest: 48
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
45% (02:23) correct
55%
(02:51)
wrong
based on 20
sessions
History
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Time
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Not Attempted Yet
Donnie’s Donuts delivers donuts by the dozen (12 per dozen) to five businesses: Fred’s Flowers, Greg’s Garage, Harold’s Chicken, John’s Juices, and Kenny’s Kitchen. Each day, Donnie delivers exactly 120 donuts. The orders are as follows: Fred’s Flowers and Greg’s Garage each order 2 dozen donuts per day, John’s Juices and Kenny’s Kitchen each order 3 dozen donuts per day, and Harold’s Chicken orders 5 dozen donuts per day.
During a certain 3-day period, each business placed at least one order, and no business placed more than two orders.
Select for Highest the highest total number of donuts a single business purchases in this period and select for Lowest the lowest total number of donuts a single business purchases in the same period.
During a certain 3-day period, each business placed at least one order, and no business placed more than two orders.
Select for Highest the highest total number of donuts a single business purchases in this period and select for Lowest the lowest total number of donuts a single business purchases in the same period.
| Highest | Lowest | |
| 24 | ||
| 36 | ||
| 48 | ||
| 72 | ||
| 96 | ||
| 120 |
ShowHide Answer
Official Answer
Highest: 120
Lowest: 48
27 Nov 2020, 07:37
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Official Solution:
Let's simplify and calculate in dozens. The orders per business are as follows:
• F = 2
• G = 2
• J = 3
• K = 3
• H = 5
Since exactly 10 dozens are delivered each day, the following five sets of deliveries, each totaling 10 dozens, are possible:
• {F, G, J, K} = 10
• {H, F, J} = 10
• {H, F, K} = 10
• {H, G, J} = 10
• {H, G, K} = 10
Notice that all three days cannot use a set with three businesses because each such set includes H, and no business places more than two orders. Therefore, one of the days must use {F, G, J, K}, and the other two days must use triplets that ensure each business places at least one order. This can be achieved with the following distribution over the three days: {F, G, J, K}, {H, F, J}, and {H, G, K}. With this, we find that each business receives exactly two orders over the three-day period.
Therefore, the highest total number of donuts purchased by a single business is for H, totaling 5 + 5 = 10 dozens = 120 donuts. The lowest total is for F or G, each totaling 2 + 2 = 4 dozens = 48 donuts.
Correct answer:
Highest "120"
Lowest "48"
Bunuel
Donnie’s Donuts delivers donuts by the dozen (12 per dozen) to five businesses: Fred’s Flowers, Greg’s Garage, Harold’s Chicken, John’s Juices, and Kenny’s Kitchen. Each day, Donnie delivers exactly 120 donuts. The orders are as follows: Fred’s Flowers and Greg’s Garage each order 2 dozen donuts per day, John’s Juices and Kenny’s Kitchen each order 3 dozen donuts per day, and Harold’s Chicken orders 5 dozen donuts per day.
During a certain 3-day period, each business placed at least one order, and no business placed more than two orders.
Select for Highest the highest total number of donuts a single business purchases in this period and select for Lowest the lowest total number of donuts a single business purchases in the same period.
During a certain 3-day period, each business placed at least one order, and no business placed more than two orders.
Select for Highest the highest total number of donuts a single business purchases in this period and select for Lowest the lowest total number of donuts a single business purchases in the same period.
| Highest | Lowest | |
| 24 | ||
| 36 | ||
| 48 | ||
| 72 | ||
| 96 | ||
| 120 |
Let's simplify and calculate in dozens. The orders per business are as follows:
• F = 2
• G = 2
• J = 3
• K = 3
• H = 5
Since exactly 10 dozens are delivered each day, the following five sets of deliveries, each totaling 10 dozens, are possible:
• {F, G, J, K} = 10
• {H, F, J} = 10
• {H, F, K} = 10
• {H, G, J} = 10
• {H, G, K} = 10
Notice that all three days cannot use a set with three businesses because each such set includes H, and no business places more than two orders. Therefore, one of the days must use {F, G, J, K}, and the other two days must use triplets that ensure each business places at least one order. This can be achieved with the following distribution over the three days: {F, G, J, K}, {H, F, J}, and {H, G, K}. With this, we find that each business receives exactly two orders over the three-day period.
Therefore, the highest total number of donuts purchased by a single business is for H, totaling 5 + 5 = 10 dozens = 120 donuts. The lowest total is for F or G, each totaling 2 + 2 = 4 dozens = 48 donuts.
Correct answer:
Highest "120"
Lowest "48"
03 Dec 2024, 06:54
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I have revised the question, solution, and formatting by adding more details to enhance clarity.
