Question

Tickets for an Amtrak train cost $21 for children and $49 for adults. Josie paid $3,332 for a total of 88 tickets. How many children tickets and how many adult tickets did Josie buy?

Answer 1

Case: System of equation word problem

Required: Find the number of adults and children tickets Josie bought.

First we create a system of equation. One for the total number of tickets, the other for the total cost of tickets.

Assumption: Let the number of adult tickets be a and the number of children tickets c.

Sytems of equations:

`\begin{gathered} a\text{ + c= 88. (ticket equation)} \\ 49a\text{ + 21c = 3332. (Cost equation)} \end{gathered}`

Solving the system of equation, using substitution method

`\begin{gathered} \text{Make c the isolated variable from ticket equation} \\ c=\text{ 88-a} \\ \text{Substitutute in Cost equation.} \\ 49a\text{ + 21c = 3332. } \\ 49a\text{ + 21(88-a) = 3332. } \\ 49a\text{ + 1848 - 21a = 3332. } \\ \text{Taking like terms} \\ 49a\text{ - 21a = 3332 - 1848} \\ 28a\text{ = }1484 \\ Divide\text{ both sides by 28} \\ a=53 \end{gathered}`

Next we find the value of c

`\begin{gathered} We\text{ plug in the value }a\text{ in the isolated variable equation} \\ c=\text{ 88 - a} \\ c=\text{ 88 - 53} \\ c=\text{ 35} \end{gathered}`

Final answers:

The total number of children tickets bought were 35 WHILE

The total number of adult tickets bought were 53.