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

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) (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

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