AMC12 2005 A
AMC12 2005 A · Q4
AMC12 2005 A · Q4. It mainly tests Money / coins, Basic counting (rules of product/sum).
A store normally sells windows at $\$100$ each. This week the store is offering one free window for each purchase of four. Dave needs seven windows and Doug needs eight windows. How many dollars will they save if they purchase the windows together rather than separately?
一家商店通常以 $\$100$ 的价格出售每个窗户。本周商店提供每购买四个窗户赠送一个免费窗户。Dave 需要七个窗户，Doug 需要八个窗户。如果他们一起购买而不是分开购买，能节省多少美元？
(A)
100
100
(B)
200
200
(C)
300
300
(D)
400
400
(E)
500
500
Answer
Correct choice: (A)
正确答案：（A）
Solution
For $n$ windows, the store offers a discount of $100 \cdot \left\lfloor\frac{n}{5}\right\rfloor$ (floor function). Dave receives a discount of $100 \cdot \left\lfloor \frac{7}{5}\right \rfloor = 100$ and Doug receives a discount of $100 \cdot \left\lfloor \frac{8}{5}\right\rfloor = 100$. These amount to $200$ dollars in discounts. Together, they receive a discount of $100 \cdot \left\lfloor \frac{15}{5} \right\rfloor = 300$, so they save $300-200=100\ \mathrm{(A)}$.
For $n$ windows, the store offers a discount of $100 \cdot \left\lfloor\frac{n}{5}\right\rfloor$ (floor function). Dave receives a discount of $100 \cdot \left\lfloor \frac{7}{5}\right \rfloor = 100$ and Doug receives a discount of $100 \cdot \left\lfloor \frac{8}{5}\right\rfloor = 100$. These amount to $200$ dollars in discounts. Together, they receive a discount of $100 \cdot \left\lfloor \frac{15}{5} \right\rfloor = 300$, so they save $300-200=100\ \mathrm{(A)}$.
Topics
Related Questions
Practice full AMC exams on amcdrill.
Try full-length practice and diagnostics at www.amcdrill.com.