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 can compare the ratios of the number of tickets to the total cost for each scenario:
For 20 tickets: 20 tickets / $250 = $12.50 per ticket
For 30 tickets: 30 tickets / $375 = $12.50 per ticket
For 50 tickets: 50 tickets / $625 = $12.50 per ticket
Since the cost per ticket is the same ($12.50) for all three scenarios, 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 ratio we determined earlier: $12.50 per ticket.
For 32 tickets: 32 tickets * $12.50 per ticket = $<<32*12.50=400>>400 total cost
For 36 tickets: 36 tickets * $12.50 per ticket = $<<36*12.50=450>>450 total cost
For 40 tickets: 40 tickets * $12.50 per ticket = $<<40*12.50=500>>500 total cost
Therefore, the total cost for 32 tickets is $400, for 36 tickets is $450, and for 40 tickets is $500.
c. Let's write an equation to find the total cost, represented by y, of x museum tickets. Based on the given information, we know that the cost per ticket is $12.50. Let's represent the number of tickets as x:
Total cost of x tickets = $12.50 * x
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 substitute the total cost ($800) into the equation we derived in part c:
$800 = $12.50x
To isolate x (number of tickets) on one side of the equation, we can divide both sides by $12.50:
$800 / $12.50 = x
64 = x
So, Mr. Jenkins buys 64 tickets for the class trip.
a. To determine if the cost of each ticket is the same, we can compare the prices for different quantities of tickets.
Let's calculate the cost per ticket for each scenario:
For 20 tickets costing $250: Cost per ticket = $250 / 20 = $12.50
For 30 tickets costing $375: Cost per ticket = $375 / 30 = $12.50
For 50 tickets costing $625: Cost per ticket = $625 / 50 = $12.50
Since the cost per ticket is the same for all three scenarios ($12.50), 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 refer to the given prices and use interpolation to estimate the costs.
Let's create a table with the number of tickets and their corresponding total costs:
Number of Tickets | Total Cost
----------------- | ----------
20 | $250
30 | $375
50 | $625
Using interpolation, we can estimate the total cost for 32 tickets:
Total Cost for 32 tickets = (($375 - $250) / (30 - 20)) * (32 - 20) + $250
= ($125 / 10) * 12 + $250
= $15 * 12 + $250
= $180 + $250
= $430
Similarly, we can estimate the total cost for 36 tickets:
Total Cost for 36 tickets = (($625 - $375) / (50 - 30)) * (36 - 30) + $375
= ($250 / 20) * 6 + $375
= $12.50 * 6 + $375
= $75 + $375
= $450
And we can estimate the total cost for 40 tickets:
Total Cost for 40 tickets = (($625 - $375) / (50 - 30)) * (40 - 30) + $375
= ($250 / 20) * 10 + $375
= $12.50 * 10 + $375
= $125 + $375
= $500
The table of values would be:
Number of Tickets | Total Cost
----------------- | ----------
32 | $430
36 | $450
40 | $500
c. To write an equation to find the total cost (y) of x museum tickets, we need to use the concept of linear equations.
We can observe that the total cost depends on the number of tickets, so let's use "x" to represent the number of tickets.
From the given prices, we can see that a linear equation in the form of y = mx + b can represent the relationship between the number of tickets (x) and the total cost (y).
Let's find the slope (m):
m = (change in y) / (change in x) = ($625 - $250) / (50 - 20) = $375 / 30 = $12.50
Now, let's find the y-intercept (b):
We can choose any given point; let's use (20, $250):
$250 = ($12.50 * 20) + b
$250 = $250 + b
b = $0
Therefore, the equation to find the total cost (y) of x museum tickets is:
y = $12.50x
d. Mr. Jenkins spends $800 on museum tickets for the class trip. We can use the equation we wrote in part c to find how many tickets Mr. Jenkins buys.
$800 = $12.50x
To solve for x, we can divide both sides of the equation by $12.50:
$800 / $12.50 = x
x = 64
Therefore, Mr. Jenkins buys 64 museum tickets for the class trip.
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
However, I will start you out.
a. Does 250/20 = 375/30 = 625/50?