Question

In the following exercises, translate to a system of equations and solve.

Tickets for a train cost \(10 for children and \)22 for adults. Josie paid $1,200 for a total of 72 tickets. How many children’s tickets and how many adult tickets did Josie buy?

Short answer

The number of children tickets are 40 and number of adult tickets are 32.

Step-by-step solution

Step 1. Given Information   

The given data is that Tickets for a train cost $10 for children and $22 for adults. Josie paid $1,200 for a total of 72 tickets.

Step 2. Calculation  

Let x be the number of adult tickets and ybe the number of child tickets.

Total number of tickets is 72 that is $x+y=72--\left(1\right)$

The total amount paid for tickets is $1200 that can be expressed as $22x+10y=1200--\left(2\right)$

Multiply equation (1) with 10 and write the revised equation.

$$\begin{gathered} 10(x+y)=10\left(72\right) \\ 10x+10y=720--\left(3\right) \end{gathered}$$

Solve the equations (2) and (3) by subtracting equation (3) from equation (2) to find the value of x.

$$\begin{gathered} 22x+10y-10x-10y=1200-720 \\ 12x=480 \\ x=40 \end{gathered}$$

Substitute the value of x in equation (1) to find the value of y.

$$\begin{gathered} 40+y=72 \\ y=72-40 \\ y=32 \end{gathered}$$