The cost of admission to Fantasy World theme park

Question

The cost of admission to Fantasy World theme park totalled $120.50 for a group of 11 children and 2 adults.

The admission totalled $100 for another group consisting of 7 children and 3 adults. Determine the cost for an

adult and for a child admission ticket.

Answer 1

A = cost for adults

B = cost for children

 

Given:

 

(i)   2A + 11C = 120.50

(ii)  3A + 7C = 100

 

Just solve the above 2 equations in 2 unknowns A and C.

 

From (ii) get A = (100 - 7C)/3 and substitute into (i) to get C.

 

2(100 - 7C)/3 + 11C = 120.50

 

C = 8.50

A = (100 - 7*8.50)/3 = 13.50

 

Children: $8.50

Adult:  $13.50 

 

 

Answer 2

C = cost of one  child ticket,  A = cost of one adult ticket

 

     11C + 2A  = $120.50

 

       7C + 3A  = $100

 

Multiply top equation by 3:          33C +   6A   = $361.50

 

Multiply bottom equation by -2: -14C + (-6A) = -$200

 

Combine equations:                    19C              = $161.50

 

                                                              C      = $8.50

 

                                                              A      = $13.50