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 $ 115.Two adults and three children must pay $ 82.Find the price of the? adult's ticket and the price of a? child's ticket.

Answer 1

Let;

a = cost of adult ticket

c = cost of child's ticket

 

Three adults and four children must pay $ 115

 

3a + 4c = 115

 

Two adults and three children must pay $ 82

 

2a + 3c = 82

 

Now solve for one of the variables in either equation

 

2a + 3c = 822a = 82 - 3c

a = (82 - 3c)/2

 

Substitute this into the other equation and solve for c, the cost of a child's ticket

 

3a + 4c = 115

3(82 - 3c)/2 + 4c = 115

123 - 9c/2 + 4c = 115

combine like terms

123 - 115 = 9c/2 - 8c/2

8 = c/2

16 = c

 

Use the cost of a child's ticket to solve for a, cost of adult ticket.

 

3a + 4(16) = 115

3a + 64 = 115

3a = 115 - 64

3a = 51

a = 17