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Question
The table shows the number of different kinds of entrées sold at the basketball concession stand on Tuesday night.
Entrées Sold on Tuesday
Kind of Entrée Number Sold
Chili dog 6
Frito pie 16
Hot dog 8
Nachos 10
If the basketball concession stand sells 120 entrées at the basketball concession stand on Friday night, which prediction for Friday is supported by the data in the table?
Responses
A The number of nachos sold will be half the number of Frito pies sold.The number of nachos sold will be half the number of Frito pies sold.
B At least 25 hot dogs will be sold.At least 25 hot dogs will be sold.
C The number of hot dogs sold will be 6 more than the number of chili dogs sold.The number of hot dogs sold will be 6 more than the number of chili dogs sold.
D The number of nachos sold will be 6 times the number of hot dogs sold.The number of nachos sold will be 6 times the number of hot dogs sold.
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To predict the number of entrées sold on Friday night, we can look at the ratios of the different kinds of entrées sold on Tuesday night.
According to the data:
- The ratio of chili dogs to Frito pies is 6:16, or 3:8.
- The ratio of chili dogs to hot dogs is 6:8, which simplifies to 3:4.
- The ratio of chili dogs to nachos is 6:10, or 3:5.
To make a prediction for Friday night, we can use these ratios to estimate the number of each kind of entrée sold.
A. The number of nachos sold will be half the number of Frito pies sold.
Based on the ratios, if there were 16 Frito pies sold, we would expect there to be (5/8) * 16 = 10 nachos sold. However, this does not match the data in the table, as there were only 10 nachos sold on Tuesday. Therefore, option A is not supported by the data.
B. At least 25 hot dogs will be sold.
Based on the ratios, if there were 8 hot dogs sold, we would expect there to be (4/3) * 8 = 10.67 chili dogs sold. However, since the number of chili dogs sold must be a whole number, it is not possible to have 10.67 chili dogs sold. Therefore, option B is not supported by the data.
C. The number of hot dogs sold will be 6 more than the number of chili dogs sold.
Based on the ratios, if there were 6 chili dogs sold, we would expect there to be (4/3) * 6 = 8 hot dogs sold, which matches the data in the table. Therefore, option C is supported by the data.
D. The number of nachos sold will be 6 times the number of hot dogs sold.
Based on the ratios, if there were 8 hot dogs sold, we would expect there to be (5/3) * 8 = 13.33 nachos sold. However, since the number of nachos sold must be a whole number, it is not possible to have 13.33 nachos sold. Therefore, option D is not supported by the data.
In conclusion, the prediction for Friday that is supported by the data in the table is that the number of hot dogs sold will be 6 more than the number of chili dogs sold.