Question

. BASKETBALL In 2005, the average ticket prices for Dallas Mavericks games and Boston Celtics games are shown in the table below. The change in price is from the 2004 season to the 2005 season. Team Average Ticket Price Change in Price Dallas $53.60 $0.53 Boston $55.93 –$1.08

a. Assume that tickets continue to change at the same rate each year after 2005. Let x be the number of years after 2005, and y be the price of an average ticket. Write a system of equations to represent the information in the table. b. In how many years will the average ticket price for Dallas approximately equal that of Boston?

Answer 1

Answer: a. Let x be the number of years after 2005, and y be the price of an average ticket. Then, we can write the following system of equations to represent the information in the table:

For Dallas:

y = 53.60 + 0.53x

For Boston:

y = 55.93 - 1.08x

This system of equations represents the average ticket price y for Dallas and Boston as a function of the number of years x after 2005, with the change in price from the 2004 season to the 2005 season given in the table.

b. To find the number of years when the average ticket price for Dallas will approximately equal that of Boston, we can set the two equations equal to each other and solve for x:

53.60 + 0.53x = 55.93 - 1.08x

2.33x = 2.33

x = 1

So, the average ticket price for Dallas and Boston will approximately equal each other after 1 year. Therefore, in 2006, the average ticket price for Dallas will approximately equal that of Boston.

Explanation:

Answer 2

a. Let's call the average ticket price for Dallas in 2005 as "d" and the average ticket price for Boston in 2005 as "b". Then the system of equations can be written as:

y_d = d + 0.53x (where y_d represents the price of an average ticket for Dallas after x years)

y_b = b - 1.08x (where y_b represents the price of an average ticket for Boston after x years)

b. To find the number of years in which the average ticket price for Dallas will approximately equal that of Boston, we need to solve the equation y_d = y_b for x. Plugging in the equations for y_d and y_b, we get:

d + 0.53x = b - 1.08x

Rearranging and solving for x, we have:

1.61x = b - d

x = (b - d) / 1.61

Now we just need to plug in the values for d and b from the table:

d = 53.60

b = 55.93

x = (55.93 - 53.60) / 1.61 = 2.33 years

So it will take approximately 2.33 years for the average ticket price for Dallas to approximately equal that of Boston.

Explanation: