Mr. Jenkins is going to buy museum tickets for a class trip. The museum director quotes him the following prices:
• 20 tickets cost a total of $250.
• 30 tickets cost a total of $375.
• 50 tickets cost a total of $625.
a. Based on these prices, is the cost of each ticket the same? Explain how you know.
b. Make a table of values to find the total cost of 32, 36, and 40 tickets.
c. Write an equation to find the total cost, represented by y, of x museum tickets.
d. Mr. Jenkins spends $800 on museum tickets for the class trip. Use the equation you wrote to find how many tickets Mr. Jenkins buys. Show your work or explain how you know.
a. To determine if the cost of each ticket is the same, we need to compare the cost per ticket for different quantities. From the given information, we have three total costs for different quantities of tickets. Let's calculate the cost per ticket for each case:
For 20 tickets costing $250, the cost per ticket is $250/20 = $12.50.
For 30 tickets costing $375, the cost per ticket is $375/30 = $12.50.
For 50 tickets costing $625, the cost per ticket is $625/50 = $12.50.
As we can see, the cost per ticket is the same for all three cases. Therefore, we can conclude that the cost of each ticket is the same.
b. To find the total cost of 32, 36, and 40 tickets, we can use the information given in the question. However, since we don't have the exact prices for these quantities, we need to make some assumptions based on the given data.
From the given data:
20 tickets cost $250
30 tickets cost $375
50 tickets cost $625
We can calculate the cost per ticket as $250/20 = $12.50, $375/30 = $12.50, and $625/50 = $12.50. Since the cost per ticket is the same, we can assume that the pattern continues, and the cost per ticket remains $12.50.
Using this assumption, we can calculate the total cost for 32, 36, and 40 tickets as follows:
- For 32 tickets, the total cost would be $12.50 x 32 = $400.
- For 36 tickets, the total cost would be $12.50 x 36 = $450.
- For 40 tickets, the total cost would be $12.50 x 40 = $500.
c. To write an equation to find the total cost (y) of x museum tickets, we can utilize the information given. We know that the cost per ticket is $12.50. Hence, we can write the equation as follows:
Total Cost (y) = x * Cost per ticket
Or,
y = 12.50x
d. Mr. Jenkins spends $800 on museum tickets for the class trip. To find how many tickets Mr. Jenkins buys, we can use the equation we wrote in part c:
y = 12.50x
Given that the total cost (y) is $800, we can substitute this value into the equation:
800 = 12.50x
To find the value of x, we can now solve for it by dividing both sides of the equation by 12.50:
800/12.50 = x
This simplifies to:
64 = x
Therefore, Mr. Jenkins buys 64 museum tickets for the class trip to spend $800.