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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?

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Final answer:

Denise bought 32 children's tickets and 40 adult tickets. We used a system of equations to find that there were 32 children's tickets at $10 each and 40 adult tickets at $22 each to total $1200 for 72 tickets.

Step-by-step explanation:

To solve the problem of how many children and adult tickets Denise bought, we can set up a system of equations based on the given information. Let's designate C as the number of children's tickets and A as the number of adult tickets.

According to the problem, we have two key pieces of information:

  • The cost for children tickets is $10 each and for adults, $22 for each, leading to the equation: 10C + 22A = 1200 (1) which represents the total amount spent.
  • Denise bought a total of 72 tickets, giving us the equation: C + A = 72 (2) which represents the total number of tickets.

We need to solve this system to find the values of C and A. By manipulating equation (2), we can express A as A = 72 - C and substitute it into equation (1).

Substituting A in equation (1):

10C + 22(72 - C) = 1200

Now, let's solve for C:

10C + 1584 - 22C = 1200

-12C = 1200 - 1584

-12C = -384

C = 32

Now we know there were 32 children's tickets. We can use this number to find the number of adult tickets:

A = 72 - C

A = 72 - 32

A = 40

So, Denise bought 32 children's tickets and 40 adult tickets.

User DarkThrone
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