AMC 8 2019 Problem 1 | Number Counting Problem

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?

• 6
• 7
• 8
• 9
• 10

AMC 8 2019 Problem 1

9

Try to start with

Let $s$ be the number of sandwiches and $d$ be the number of sodas. So it we will have
$$
4.50 s+d=30
$$

Now look , Ike and Mike buys maxixmum number of sandwitch possible, we can say $4.50s=30$ but s is integrer so the maximum s can be is 6 that is $4.50 \times 6 = 27$ So, $\$ 3.00$ is remaining.

So, the number if sodas is 3,

So, The number of items will be,

$6+3=9$

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