SOLUTION: a group of four students decide to hire a tutor for a review session prior to an examination, and the tutor's fee is to be shared by each student. if two additional students join t

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Question 778895: a group of four students decide to hire a tutor for a review session prior to an examination, and the tutor's fee is to be shared by each student. if two additional students join the group, the cost to each student is reduced by $6. what is the cost per student if four are in the group?
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a group of four students decide to hire a tutor for a review session prior to an examination, and the tutor's fee is to be shared by each student. if two additional students join the group, the cost to each student is reduced by $6. what is the cost per student if four are in the group?

Ans:
Let the total fees be x.
With 4 students, each student's share is x/4
With 2 more i.e. 6 students, each student's share is x/6, which is clearly
lower then x/4.
Difference between the two is given as $6.So we have the equation
x%2F4+-+x%2F6+=+6
Multiplying both sides by LCM of 4 and 6 which is 12
3%2Ax+-+2%2Ax+=+6%2A12+=+72
x+=+72
Total tuition fees = $72
Cost per student if 4 students are there = 72/4 = $18.
(Check: If 6 students are there, the cost per student = 72/6 = 12, which is $6
lower than the per-student cost for 4 students)
:)