AMC12 2009 B

AMC12 2009 B · Q1

AMC12 2009 B · Q1. It mainly tests Money / coins, Divisibility & factors.

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晨，都会买一个 $50$ 美分的松饼或一个 $75$ 美分的百吉饼。她这一周的总花费是整数美元。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

If Jane bought one more bagel but one fewer muffin, then her total cost for the week would increase by $25$ cents. If Jane bought $1$ bagel, then she bought $4$ muffins. Her total cost for the week would be $75\cdot1+50\cdot4=275$ cents, or $2.75$ dollars. Clearly, she bought one more bagel but one fewer muffin at a total cost of $3.00$ dollars. Therefore, she bought $\boxed{\textbf{(B) } 2}$ bagels.

如果 Jane 多买 $1$ 个百吉饼而少买 $1$ 个松饼，那么她这一周的总花费将增加 $25$ 美分。如果 Jane 买了 $1$ 个百吉饼，那么她买了 $4$ 个松饼。她这一周的总花费为 $75\cdot1+50\cdot4=275$ 美分，即 $2.75$ 美元。显然，她再多买一个百吉饼并少买一个松饼时，总花费为 $3.00$ 美元。因此，她买了 $\boxed{\textbf{(B) } 2}$ 个百吉饼。

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