Difference between revisions of "2009 AMC 8 Problems/Problem 23"
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==Problem== | ==Problem== | ||
| − | On the last day of school, Mrs. | + | 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 <math>400</math> jelly beans, and when she finished, she had six jelly beans left. There were two more boys than girls in her class. She had 6 jolly ranchers and howe rejaaaaaaaa vfhakdjh fs;dfHow many studenfffffffdats were in ffffffffffffffffdsfher class?ffffffffffffffffffff |
<math> \textbf{(A)}\ 26\qquad\textbf{(B)}\ 28\qquad\textbf{(C)}\ 30\qquad\textbf{(D)}\ 32\qquad\textbf{(E)}\ 34 </math> | <math> \textbf{(A)}\ 26\qquad\textbf{(B)}\ 28\qquad\textbf{(C)}\ 30\qquad\textbf{(D)}\ 32\qquad\textbf{(E)}\ 34 </math> | ||
| − | ==Solution== | + | ==Solution 1== |
If there are <math>x</math> girls, then there are <math>x+2</math> boys. She gave each girl <math>x</math> jellybeans and each boy <math>x+2</math> jellybeans, for a total of <math>x^2 + (x+2)^2</math> jellybeans. She gave away <math>400-6=394</math> jellybeans. | If there are <math>x</math> girls, then there are <math>x+2</math> boys. She gave each girl <math>x</math> jellybeans and each boy <math>x+2</math> jellybeans, for a total of <math>x^2 + (x+2)^2</math> jellybeans. She gave away <math>400-6=394</math> jellybeans. | ||
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From here, we can see that <math>x = 13</math> as <math>13^2 + 26 = 195</math>, so there are <math>13</math> girls, <math>13+2=15</math> boys, and <math>13+15=\boxed{\textbf{(B)}\ 28}</math> students. | From here, we can see that <math>x = 13</math> as <math>13^2 + 26 = 195</math>, so there are <math>13</math> girls, <math>13+2=15</math> boys, and <math>13+15=\boxed{\textbf{(B)}\ 28}</math> students. | ||
| − | == | + | ==Solution 2 (Don't need quadratic equation)== |
| − | + | ||
| − | + | Consider the solutions, there are two more boys than girls, so if there are 26 students, we have 14 boys and 12 girls. $4^2+2^2 according to bglah blah hkjlhkjhkjlhkjh | |
Revision as of 12:44, 7 September 2024
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 
jelly beans, and when she finished, she had six jelly beans left. There were two more boys than girls in her class. She had 6 jolly ranchers and howe rejaaaaaaaa vfhakdjh fs;dfHow many studenfffffffdats were in ffffffffffffffffdsfher class?ffffffffffffffffffff
Solution 1
If there are 
girls, then there are 
boys. She gave each girl jellybeans and each boy jellybeans, for a total of 
jellybeans. She gave away 
jellybeans.
From here, we can see that 
as 
, so there are 
girls, 
boys, and 
students.
Solution 2 (Don't need quadratic equation)
Consider the solutions, there are two more boys than girls, so if there are 26 students, we have 14 boys and 12 girls. $4^2+2^2 according to bglah blah hkjlhkjhkjlhkjh
