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2019 AMC 8 Problems/Problem 1

Revision as of 23:42, 19 November 2019 by Eth007 (talk | contribs) (→‎Solution 1)

Problem 1

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?

$\textbf{(A) }6\qquad\textbf{(B) }7\qquad\textbf{(C) }8\qquad\textbf{(D) }9\qquad\textbf{(E) }10$

Solution 1

We maximize the number of sandwiches Mike and Ike can buy by finding the lowest multiple of $$4.50$ that is less than $$30.$ This number is $6.$

Therefore, they can buy $6$ sandwiches for $$4.50\cdot6=$27.$ They spend the remaining money on soft drinks, so they buy $30-27=3$ soft drinks.

Combining the items, Mike and Ike buy $6+3=9$ soft drinks.

The answer is $\boxed{\textbf{(D) }9}.$

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