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

The correct answer is:

c) 69.5𝑥 + 48.5𝑦 = 538.5
𝑥 + 𝑦 = 11

Answer 2

The correct system of equations that could be used to find the number of adult tickets (x) and the number of children's tickets (y) purchased is:

c) 69.5x + 48.5y = 538.5
x + y = 11

Answer 3

The correct system of equations to find the number of adult tickets purchased (x) and the number of children's tickets purchased (y) would be:

c) 69.5x + 48.5y = 538.5
x + y = 11

Let's break it down and explain why this is the correct system of equations:

The problem states that the Polar Express charges $69.50 per adult ticket and $48.50 per child's ticket. This means that for every adult ticket purchased, the cost would be $69.50, and for every child's ticket purchased, the cost would be $48.50.

Let's consider the number of adult tickets purchased as x and the number of children's tickets purchased as y.

The total cost of tickets purchased by the group can be expressed as $538.50. This gives us the equation:

69.5x + 48.5y = 538.5

The equation above represents the total cost as the sum of the adult tickets' cost (69.5x) and the children's tickets' cost (48.5y).

The problem also states that there were 11 people in the group. Since the group is comprised of adults and children, the total number of people can be expressed as the sum of the number of adult tickets purchased (x) and the number of children's tickets purchased (y). This gives us the equation:

x + y = 11

So, the correct system of equations to find x and y is:

69.5x + 48.5y = 538.5
x + y = 11

Therefore, option c) 69.5x + 48.5y = 538.5 and x + y = 11 is the correct system of equations.