algebra 1 word problem

Question

Jen butler has been pricing Speed-Pass train fares for a goeuo trip to New York. three adults and four children must pay $136. Two adults and three children must pay $97. Find the price of the adults ticket and the price of a child's ticket.

Answer 1

A - adult price

 

C - child price

 

3A + 4C = 136    (1)

 

and

 

2A + 3C = 97      (2)

 

Multiply both sides of (1) by 2:

 

6A + 8C = 272     (3)

 

Next, multiply both sides of (2) by 3:

 

6A + 9C = 291      (4)

 

Next, calculate (4) - (3):

 

(6-6)A +(9-8)C = (291-272)     (5)

 

C  = 19                (6)

 

So, the child price is $19.

 

Next, solve (2) for A:

 

2A = 97 - 3C         (7)

 

A = (97- 3C)/2      (8)

 

Nest, plug in the result of (6)

 

A = (97 - 3(19))/2     (9)

 

A = (97 - 57)/2          (10)

 

A = 40/2                   (11)

 

A = 20                      (12)

 

So, the adult price is $20