The Polar Express charges $69.50 per adult ticket and $48.50 per child’s ticket. A group of 11

Question

The Polar Express charges $69.50 per adult ticket and $48.50 per child’s ticket. A group of 11

people paid $538.50 for tickets. Which system of equations could be used to find x, the number
of adult tickets purchased, and y, the number of children's tickets purchased?
a) 48. 5𝑥 + 69. 5𝑦 = 538. 5
𝑥 + 𝑦 = 11
b) 48. 5𝑥 + 69. 5𝑦 = 11
𝑥 + 𝑦 = 538. 5
c) 69. 5𝑥 + 48. 5𝑦 = 538. 5
𝑥 + 𝑦 = 11
d) 69. 5𝑥 + 48. 5𝑦 = 11
𝑥 + 𝑦 = 538. 5

Answer 1

c) 69.5𝑥 + 48.5𝑦 = 538.5

𝑥 + 𝑦 = 11

Answer 2

The correct system of equations would be:

c) 69.5𝑥 + 48.5𝑦 = 538.5
𝑥 + 𝑦 = 11

Answer 3

To solve this problem, we need to set up a system of equations to represent the given information. Let's define the variables x and y as the number of adult tickets and children's tickets purchased, respectively.

The cost of each adult ticket is $69.50, so the total cost of adult tickets can be found by multiplying the ticket price by the number of adult tickets:
69.50x

Similarly, the cost of each child's ticket is $48.50, so the total cost of children's tickets can be found by multiplying the ticket price by the number of children's tickets:
48.50y

The total amount paid for tickets is $538.50, so we can set up the first equation as:
69.50x + 48.50y = 538.50

The second equation can be set up to represent the total number of people in the group, which is equal to the sum of the number of adult tickets and the number of children's tickets:
x + y = 11

Now let's look at the answer choices:

a) 48.5𝑥 + 69.5𝑦 = 538.5
𝑥 + 𝑦 = 11

This choice has the correct form for both equations, with the cost equation and the total people equation.

b) 48.5𝑥 + 69.5𝑦 = 11
𝑥 + 𝑦 = 538.5

This choice has the equations reversed, with the cost equation incorrectly set up as 11 instead of 538.5.

c) 69.5𝑥 + 48.5𝑦 = 538.5
𝑥 + 𝑦 = 11

This choice has the correct form for both equations, with the cost equation and the total people equation.

d) 69.5𝑥 + 48.5𝑦 = 11
𝑥 + 𝑦 = 538.5

This choice also has the equations reversed, with the cost equation incorrectly set up as 11 instead of 538.5.

From the analysis, the correct system of equations is:

69.5𝑥 + 48.5𝑦 = 538.5
𝑥 + 𝑦 = 11

Therefore, the answer is option a).