To predict the number of cheese slices sold, we need to find the percentage of patrons who prefer cheese out of all the patrons surveyed.
Number of cheese-loving patrons: 9
Total number of patrons surveyed: 9 + 5 + 6 + 7 = 27
Percentage of cheese-loving patrons: (9/27) * 100% = 33.3%
Now, to predict the number of cheese slices sold out of 1,299 slices, we multiply the total number of slices by the percentage of cheese-loving patrons:
1,299 * 0.333 = 432.867
Therefore, we predict that approximately 433 cheese slices will be sold.
Answer: 433 patrons