Problem:
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?
Answer Choices:
A. 26
B. 28
C. 30
D. 32
E. 34
Solution:
Mrs. Wonderful gave 400−6=394 jelly beans to the class. Make a table, starting with a small, reasonable number of girls and boys.
Girls910111213Boys1112131415Number 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.
Answer: B.
The problems on this page are the property of the MAA's American Mathematics Competitions