2019 AMC 8

Complete problem set with solutions and individual problem pages

Problem 1 Easy

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 any remaining money to buy soft drinks. Counting both sandwiches and soft drinks, how many items will they buy?

  • A.

    6

  • B.

    7

  • C.

    8

  • D.

    9

  • E.

    10

Answer:D

Solution 1

We know that the sandwiches cost 4.50 dollars. Guessing will bring us to multiplying 4.50 by 6, which gives us 27.00. Since they can spend 30.00 they have 3 dollars left. Since soft drinks cost 1.00 dollar each, they can buy 3 soft drinks, which makes them spend 30.00 Since they bought 6 sandwiches and 3 soft drinks, they bought a total of 9 items. Therefore, the answer is \boxed{\textbf{(D) }9}.

 

Solution 2

Let s be the number of sandwiches and d be the number of sodas. We have to satisfy the equation of4.50s+d=30In the question, it states that Ike and Mike buys as many sandwiches as possible. So, we drop the number of sodas for a while. We have:

\begin{align*} 4.50s&=30 \\ s&=\frac{30}{4.5} \\ s&=6R3 \end{align*}

We don't want a remainder so the maximum number of sandwiches is 6. The total money spent is 6\cdot 4.50=27. The number of dollar left to spent on sodas is 30-27=3 dollars. 3 dollars can buy 3 sodas leading us to a total of 6+3=9 items. Hence, the answer is \boxed{\textbf{(D) }9}.

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