AMC10 2009 B

AMC10 2009 B · Q1

AMC10 2009 B · Q1. It mainly tests Money / coins, Remainders & modular arithmetic.

Each morning of her five-day workweek, Jane bought either a 50-cent muffin or a 75-cent bagel. Her total cost for the week was a whole number of dollars. How many bagels did she buy?

Jane 在她五天工作周的每个早上，买了一个50美分的松饼或一个75美分的百吉饼。她一周的总花费是一个整数组美元。她买了多少个百吉饼？

(A) 1 1

(B) 2 2

(D) 4 4

(E) 5 5

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): Make a table for the cost of the muffins and bagels: \[ \begin{array}{|c|c|c|} \hline \text{Cost of Muffins} & \text{Cost of Bagels} & \text{Total Cost} \\ \hline 0\cdot 0.50 = 0.00 & 5\cdot 0.75 = 3.75 & 3.75 \\ \hline 1\cdot 0.50 = 0.50 & 4\cdot 0.75 = 3.00 & 3.50 \\ \hline 2\cdot 0.50 = 1.00 & 3\cdot 0.75 = 2.25 & 3.25 \\ \hline 3\cdot 0.50 = 1.50 & 2\cdot 0.75 = 1.50 & 3.00 \\ \hline 4\cdot 0.50 = 2.00 & 1\cdot 0.75 = 0.75 & 2.75 \\ \hline 5\cdot 0.50 = 2.50 & 0\cdot 0.75 = 0.00 & 2.50 \\ \hline \end{array} \] The only combination which is a whole number of dollars is the cost of 3 muffins and 2 bagels.

答案（B）：制作一个松饼和百吉饼成本的表格： \[ \begin{array}{|c|c|c|} \hline \text{松饼的成本} & \text{百吉饼的成本} & \text{总成本} \\ \hline 0\cdot 0.50 = 0.00 & 5\cdot 0.75 = 3.75 & 3.75 \\ \hline 1\cdot 0.50 = 0.50 & 4\cdot 0.75 = 3.00 & 3.50 \\ \hline 2\cdot 0.50 = 1.00 & 3\cdot 0.75 = 2.25 & 3.25 \\ \hline 3\cdot 0.50 = 1.50 & 2\cdot 0.75 = 1.50 & 3.00 \\ \hline 4\cdot 0.50 = 2.00 & 1\cdot 0.75 = 0.75 & 2.75 \\ \hline 5\cdot 0.50 = 2.50 & 0\cdot 0.75 = 0.00 & 2.50 \\ \hline \end{array} \] 唯一使总价为整数美元的组合是：3 个松饼和 2 个百吉饼。

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