06/01/2020 (2019: AMC 8, Problem 1)

Q: Ike and Mike go into a sandwich shop with a total of $30.00 to spend. Sandwiches cost $4.50 each and soft drinks cost $1.00 each. Ike and Mike plan to buy as many sandwiches as they can and use the remaining money to buy soft drinks. Counting both soft drinks and sandwiches, how many items will they buy?

           They are attempting to buy as  many sandwiches as possible with $30, and each sandwich costs $4.50, so we see how many times 4.5 can 'fit' into 30. 30 ÷ 4.5 = 6 2/3 ≈ 6. If they buy 6 sandwiches, they will have spent 6 ⋅ $4.50 = $27.

They spent 27 out of the 30 dollars they had, meaning that they have $3 left. Because each soft drink costs $1, that means they will buy 3 ÷ 1 drinks = 3 drinks.

3 drinks + 6 sandwiches = 9 items, making the answer D.