Every 8th person that goes into a store gets a free bottle. Every 10th person that goes into a store gets a t-shirt. There are 100 bottles and 100 t shirts to give out. How many people get a t shirt and a bottle

25 persons will get both bottle and t – shirt. Solution:Given, every 8th person that goes into a store gets a free bottle.  And every 10th person that goes into a store gets a t-shirt.  There are 100 bottles and 100 t shirts to give out.  We have to find how many people get a t shirt and a bottle Now, as there are 100 t- shirts, last person to get t – shirt is:10 x 100 = 1000th person will get last t – shirt We have to find lcm of 8 and 10, to know who gets both bottle and t – shirt. So, L.C.M of 8 and 10 = lcm(8, 10)  = 2 x lcm(4, 5)  = 2 x 4 x 5 [ as no common factors available for 4 and 5 ]= 40 So, every 40th person will get both bottle and t – shirt. Then, out of 1000 people, number of people who get both bottle and t – shirt = [tex]\frac{1000}{40} = 25[/tex]