Question

Tickets for an Amtrak train cost $10 for children and $22 for adults. Denise paid $1200 for a total of 72 tickets. How many children tickets and how many adult tickets did Denise buy? Denise bought child tickets and adult tickets.

Answer 1

Denise bought 24 child tickets and 48 adult tickets.

Step-by-step explanation:

Let's assume that Denise bought x child tickets and y adult tickets.

According to the given information, child tickets cost $10 each and adult tickets cost $22 each. We can set up the following equations:

x + y = 72 (eq. 1)

10x + 22y = 1200 (eq. 2)

To solve this system of equations, we can multiply eq. 1 by 10 and subtract it from eq. 2 to eliminate x:

10x + 10y = 720 (eq. 3)

10y - 10y = 480 (eq. 4)

Simplifying eq. 4, we get 10y = 480. Solving for y, we find that y = 48.

Substituting y = 48 into eq. 1, we can solve for x:

x + 48 = 72

x = 72 - 48

x = 24

Therefore, Denise bought 24 child tickets and 48 adult tickets.