Question

A group of church members charted a bus for $832. After making the arrangements, six more members decided to join the excursion and pay their fair share of the cost of the bus. The cost per person was reduced by $6. Find the original number of church members in the group and the original cost per member.

Answer 1

Let the initial members be x.

Total fare = 832

Share per head = 832/x

6 more members joined newly. So total x+6 members.

Share per head should be 832/(x+6).........(a)

But given that it got reduced by $6 to that of original share per person.

Original share = 832/x . It reduced by $6.

Implies, (832/x)-6.........(b)

As we observe a and b should be equal as both represents share of newly formed group per person.

Equating both,

(832/x)-6 = 832/(x+6)

832/x = 832/(x+6) + 6

832/x = 832+6x+36/(x+6)

Cross multiplying on both sides gives us,

832x + (832*6)= 832x+36x+6x²

Cancelling out 832x and 6 will give,

832 = 6x+x²

XX2-26x+32x-832 =0

fron above factorization, we get x =26 or -32

but negative people not possible so, x=26 persons is answer.

Original cost per person = 832/26 = $32 per person.