Letitia, Brianne, and Jake met at the mall on December 31. Letitia said that she intends...

 

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Letitia, Brianne, and Jake met at the mall on December 31. Letitia said that she intends to come to the mall every seventh day throughout the next year. Brianne said that she intends to be there every fourth day, and Jake said that he would be there every fifth day. Letitia said that she knew she would be at the mall a total of 52 days, since 365-7 is 52 with a remainder of 1. Brianne said that she'd be at the mall 91 days, since 365 +4 is 91 with a remainder of 1. Moreover, Brianne said that of those 91 days, she would expect to see Letitia 13 times, since they will both be coming every 28 days and 365-28 is 13 with a remainder of 1. (a) How many days will all three friends meet at the mall in the next year? There will be 2 day(s) when all three meet. (b) Use reasoning similar to that of Letitia and Brianne to construct a three-loop Venn diagram that shows the number of times the three friends go to the mall in all of the possible combinations. A. B. O.C. D. L B B B 33 28 64 31 11 62 52 13 91 7 28 41 35 20 140 8 16 10 18 35 20 30 49 47 73 5 365 188 365 126 (c) How many days in a year will Jake be at the mall by himself? There will be day(s) when Jake is at the mall by himself. Letitia, Brianne, and Jake met at the mall on December 31. Letitia said that she intends to come to the mall every seventh day throughout the next year. Brianne said that she intends to be there every fourth day, and Jake said that he would be there every fifth day. Letitia said that she knew she would be at the mall a total of 52 days, since 365-7 is 52 with a remainder of 1. Brianne said that she'd be at the mall 91 days, since 365 +4 is 91 with a remainder of 1. Moreover, Brianne said that of those 91 days, she would expect to see Letitia 13 times, since they will both be coming every 28 days and 365-28 is 13 with a remainder of 1. (a) How many days will all three friends meet at the mall in the next year? There will be 2 day(s) when all three meet. (b) Use reasoning similar to that of Letitia and Brianne to construct a three-loop Venn diagram that shows the number of times the three friends go to the mall in all of the possible combinations. A. B. O.C. D. L B B B 33 28 64 31 11 62 52 13 91 7 28 41 35 20 140 8 16 10 18 35 20 30 49 47 73 5 365 188 365 126 (c) How many days in a year will Jake be at the mall by himself? There will be day(s) when Jake is at the mall by himself.