word problem

Question

jen butler has been pricing speed pass train fares for a group trip to new york. three adults and four children must pay $90. two adults and three children must pay $64. find the price of the adults ticket and the prices of a child's ticket

Answer 1

3A + 4C = 90

2A + 3C = 64

 

Multiplies the first equation by 2 and the second by -3

 

6A + 8C = 180

-6a + -9c = -192

 

-C = -12

C = 12

 

Plugs into the first equation:

 3A + 4(12) = 90

3A + 48 = 90

3A = 42

A = 14

 

Children tix costs 12, adult tix cost 14

 

2 adults and 3 kids --> 2*14 + 3*12 = 28 + 36 = 64 <--- yes, it checks