AMC 8 2009 Problem 23
AMC8 2009 年第 23 题
特殊数与不定方程★★★☆☆
On the last day of school, Mrs. Wonderful gave jelly beans to her class. She gave each boy as many jelly beans as there were boys in the class. She gave each girl as many jelly beans as there were girls in the class. She brought 400 jelly beans, and when she finished, she had six jelly beans left. There were two more boys than girls in her class. How many students were in her class?
在学期的最后一天，苏威太太给全班同学送去了果冻豆。她给每个男孩的果冻豆数量和班上男孩的数量一样多，她给每个女孩的果冻豆数量和班上女孩的数量一样多。她一共带了 400 颗果冻豆，当她发完时，她还剩下 6 个果冻豆。她班上男生比女生多两个。她班上有多少学生？
- A.26
- B.28
- C.30
- D.32
- E.34
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
Mrs. Wonderful gave 400 − 6 = 394 400−6=394 jelly beans to the class. Make a table, starting with a small, reasonable number of girls and boys. Girls Boys Number of jelly beans 9 11 ( 9 × 9 ) + ( 11 × 11 ) = 202 10 12 ( 10 × 10 ) + ( 12 × 12 ) = 244 11 13 ( 11 × 11 ) + ( 13 × 13 ) = 290 12 14 ( 12 × 12 ) + ( 14 × 14 ) = 340 13 15 ( 13 × 13 ) + ( 15 × 15 ) = 394 Girls 9 10 11 12 13 Boys 11 12 13 14 15 Number of jelly beans (9×9)+(11×11)=202 (10×10)+(12×12)=244 (11×11)+(13×13)=290 (12×12)+(14×14)=340 (13×13)+(15×15)=394 The number of students is 13 + 15 = 28 13+15=28. Answer: 𝐵 B .
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