Problem 1 · 2019 AMC 8
Easy
Arithmetic & Operations
divisionunit-rate
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?
Show answer
Answer: D — 9 items.
Show hints
Hint 1 of 2
The plan is greedy: buy the expensive item until you can't, then the change becomes cheap items. So really only one question matters — how many sandwiches fit in $30?
Still stuck? Show hint 2 →
Hint 2 of 2
Sandwiches are the bottleneck; the leftover dollars convert 1-to-1 into sodas. Find the most sandwiches, then count whatever's left.
Show solution
Approach: greedy: max the expensive item, change becomes cheap items
- Sandwiches are the only limiting purchase, so ask how many fit: $30 ÷ $4.50 = 6 with $3 left (a 7th would need $31.50 — too much).
- Each soda is exactly $1, so the $3 leftover turns straight into 3 sodas — no arithmetic, just read it off.
- Total items: 6 + 3 = 9.
- Why this transfers: any "buy as many of A as possible, then fill with B" problem is a division-with-remainder — the quotient is the A count, the remainder funds the B's.
Mark:
· log in to save