SOLUTION: Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member i
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Question 200500: Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by $5. How many students attended the get-together?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let c=cost per individual (the cost before the students failed to arrive) and n=number of students
So the total cost is divided among n people to get
Since 5 failed to attend, this means that students showed up. Now the new cost is
Start with the given equation.
Plug in
Multiply every term by the LCD . This cancels out every denominator.
Distribute
Subtract from both sides.
Subtract from both sides.
Let's use the quadratic formula to solve for n
Start with the quadratic formula
Plug in , , and
Negate to get .
Square to get .
Multiply to get
Rewrite as
Add to to get
Multiply and to get .
Take the square root of to get .
or Break up the expression.
or Combine like terms.
or Simplify.
Since a negative amount of people doesn't make any sense, this means that the only answer is
So 25 people were going to attend but only 20 actually attended.
If you have any questions, email me at jim_thompson5910@hotmail.com.
Check out my website if you are interested in tutoring.
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