Geoff purchased an annual golf pass for a municipal golf course in his town. He pays a flat fee for the annual golf pass and then each round he plays he must pay the additional cost for a golf cart.

Question

A linear model of this situation contains the values (27 , 1,249) and (39 , 1,393), where x represents the number of times he plays each year, and y equals the total amount he spends on golf in one year.

What is the flat fee for the annual golf pass?
A.
$1,069
B.
$925
C.
$937
D.
$12

Answer 1

To find the flat fee for the annual golf pass, we can define a linear model based on the information given. The general equation for linear relationships can be represented as:

\[ y = mx + b \]

where:

• \( y \) is the total amount spent,
• \( x \) is the number of rounds played,
• \( m \) is the variable cost per round played (the cost for the golf cart),
• \( b \) is the flat fee for the annual golf pass.

From the problem, we have the points (27, 1,249) and (39, 1,393). We can use these points to find the slope \( m \):

1. Calculate the slope \( m \):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1393 - 1249}{39 - 27} = \frac{144}{12} = 12 \]

So the cost per round played (the cost of the golf cart) is $12.

2. Now, we can use one of the points to find \( b \), the flat fee. Let's use the point (27, 1249):

\[ 1249 = 12(27) + b \] \[ 1249 = 324 + b \] \[ b = 1249 - 324 = 925 \]

Therefore, the flat fee for the annual golf pass is $925.

The correct answer is B. $925.