One day the number of customers at three cafés, \"Alan\'s Diner\" (A), \"Sarah\'

Question

One day the number of customers at three cafés, "Alan's Diner" (A), "Sarah's Snackbar" (S) and "Pete's Eats" (P) was recorded and are given below. 17 were customers of Pete's Eats only 27 were customers of Sarah's Snackbar only 15 were customers of Alan's Diner only 10 were customers of Pete's Eats and Sarah's Snackbar but not Alan's Diner 8 were customers of Pete's Eats and Alan's Diner but not Sarah's Snackbar (a) Draw a Venn Diagram, using sets labelled A, S and P, that shows this information. There were 48 customers of Pete's Eats that day. (b) Calculate the number of people who were customers of all three cafés. There were 50 customers of Sarah's Snackbar that day (c) Calculate the total number of people who were customers of Alan's Diner. (d) Write down the number of customers of Alan's Diner that were also customers of Pete's Eats. (e) Find n[(S P) n A. Total 11

Explanation / Answer

Let x be customers of all 3: we know that 17+10+ 8 + x = 48 (pete’s eat)

So x = 48-35 = 13 customers choose all 3;

Let ‘y be customers of S and A; so number of customers of S =50 = 27+ 13 + 10 + y; y= 50-50 =0

So number of customers of A = 15+ 8 + 13+ 0 = 36;

No of customers of A and P = 8+ 13= 21

n [( S U P) and A’) = 27+ 17 + 10 = 54

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