Question

You can buy 1 child's ticket, 1 adult's ticket and 1 senior citizen's ticket for a minor league baseball game for $29. Tickets for adults cost 3 times as much as tickets for children. A family of 3 children, 2 adults, and 2 senior citizens pays a total of $63 for tickets to the game. Find the prices of each type of ticket.

Tickets cost:
$_ for children
$_ for adults
$_ for senior citizens.

Answer 1

By setting up a system of equations, we find that children's tickets cost $5, adult's tickets cost $15, and senior citizen's tickets cost $9.

Step-by-step explanation:

To solve this problem, we'll use algebra to set up equations based on the information given about the ticket prices and the cost for the family's tickets. Let's assign each ticket type a variable: c for children's tickets, a for adult's tickets, and s for senior citizen's tickets.

From the first statement, we know that the cost of one child's ticket, plus one adult's ticket, plus one senior's ticket is $29. We can express this with the equation:
c + a + s = 29

Additionally, we are told that an adult ticket costs three times as much as a child ticket, so we have another equation:
a = 3c

From the second statement, the family's total cost is $63 for 3 children, 2 adults, and 2 senior citizens. Therefore, the equation is:
3c + 2a + 2s = 63

Now we have a system of equations:

c + a + s = 29

a = 3c

3c + 2a + 2s = 63

Substituting a from the second equation into the first and third equations, we get:

• c + 3c + s = 29
• 3c + 2(3c) + 2s = 63

Simplifying:

• 4c + s = 29
• 9c + 2s = 63

Using the first simplified equation, we can solve for s in terms of c:

• s = 29 - 4c

Substituting into the second simplified equation:

• 9c + 2(29 - 4c) = 63

This simplifies to 9c + 58 - 8c = 63, so c = 5. Therefore, children's tickets are $5. Since adult tickets are three times the cost of children's tickets, a = 3(5) = $15. Finally, substituting c back into the equation for s, we get s = 29 - 4(5), so s = $9 for senior citizens.

Answer 2

Using a system of equations, it's determined that the cost for a child's ticket is $5, for an adult's ticket is $15, and for a senior citizen's ticket is $9.

Step-by-step explanation:

To solve this problem, let's define variables for each type of ticket. Let c be the cost of a child's ticket. Since an adult's ticket costs 3 times as much as a child's, let a = 3c. Let s be the cost of a senior citizen's ticket. Using the information given, we can set up two equations based on the total cost of tickets: c + 3c + s = $29, 3c + 2(3c) + 2s = $63. Simplifying the equations gives us: 4c + s = $29 (1), 9c + 2s = $63 (2). Now, multiply equation (1) by 2 and subtract it from equation (2): 2(4c) + 2s = 2($29), 9c + 2s = $63. After simplification : 8c + 2s = $58, - (9c + 2s = $63). We get: -c = -$5, c = $5. Now, using the value of c, we can find s from equation (1): 4(5) + s = $29, 20 + s = $29, s = $29 - 20, s = $9. Therefore, the cost for each type of ticket: Children: $5, Adults: 3($5) = $15, Senior citizens: $9