Question 132413: Some students planned for a get-together. The budget for food was $500. Five of the students failed to come becuase of the distance, and therefore the cost of food for each member increased by $5. How many students attended the get-together?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! In the beginning, there were x students, when five didn't show up, there were x - 5 students.
In the beginning, the cost per student was  but when five students didn't show up, the cost was  and this cost was $5 more than the original cost per student, so:
Need an LCD of  on the right:
Simplify the right hand numerator:
Cross-multiply:
Expand:
Collect terms and put into standard form:
Divide by 5:
 ,  , so:
 or  . A negative number for a number of students doesn't make much sense in this context, so exclude -20 as an extraneous root. There were originally 25 students, so 25 - 5 = 20 actually attended.
Check:
 ,  , and 
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