A manager gives gift cards to every 80th customer. On Saturday, 1210 customers entered, while on Sunday, 1814 customers entered. We are asked to find the number of people who received gift cards.
(1) Probably the most efficient method is to divide 1210 by 80.
(The first gift card was given to the 80th person and 80/80=1. The second to the 160th person and 160/80=2. The third to the 240th person and 240/80=3, etc...)
So 1210 divided by 80 is 15 with a remainder of 10.
15 people received gift cards on Saturday.
(2) We could set up a linear inequality where the unknown x represents the number of people receiving gift cards. Then 80x<1210 and x<15.125 so x=15.
(3) You could just keep adding, perhaps in a table, until you got to the last person:
(# customers, # gift cards): (80,1), (160,2), (240,3)...(1120,14), (1200,15)
The answer will not change, but the manager can either start counting at zero again on Sunday, or continue from the previous day making the first person in on Sunday number 11.
Again we take 1814 divided by 80 to get 22 with a remainder of 54. (With the additional 10 from Saturday we would have remainder 64, but still not enough people to give out another card.)
15 cards given out Sat with 22 cards given out Sun means that there were a total of 15+22=37 people who received gift cards.