SOLUTION: A group of students agreed that each would chip in the same amount to pay for a party that would cost $100. Then they found 5 more students interested in the party and in sharing

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Question 188494This question is from textbook
: A group of students agreed that each would chip in the same amount to pay for a party that would cost $100. Then they found 5 more students interested in the party and in sharing the expeneses. This decreased the amount each had to pay by $1. How many students were involved in the party and how much idid each student have to pay?
thanks again This question is from textbook

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the original number of students.

Then is the amount that each would have to pay.

And is the share for each student with the additional 5 students. But this is $1 less than the share for x students.

So:



Solve for x to get the original number of students, add 5 to get the new number of students, divide that number into 100 to get the per each share.

(Hint: Apply a common denominator on the right, complete the sum, then cross-multiply. You will end up with a factorable quadratic that will have one positive root and one negative root. Throw out the negative root - a party with a negative number of students is absurd. The positive root will be the original number of students.)

John