A bowling alley charges a flat `$6.50` fee for shoe and ball rental plus `$3.75` per game and `6.325` percent sales tax . If each person in a group of seven pwople has `$20` to spend on a bowling outing, and at least some members of the group must rent shoes and a ball, which inequality best describes this situation, given that the number of shoe and ball rentals is represented by r and the number of games is represented by g ?

Options

A. `1.06325(6.5r+3.75g)le 140`
B. `1.06325 (6.5r +3.7g ) le 20`
C. `21.06325((6.5)/® +(3.75)/(g))le 140`
D. `0.06325(6.5r +3.75g)le 20`

Explanation

To solve the problem, we need to formulate an inequality based on the costs associated with bowling for a group of seven people. Here’s a step-by-step breakdown of the solution:

### Step 1: Define the Variables
Let:
- \( r \) = number of shoe and ball rentals
- \( g \) = number of games played

### Step 2: Calculate the Costs
1. **Rental Cost**: The bowling alley charges a flat fee of $6.50 for shoe and ball rental. Therefore, the total rental cost for \( r \) rentals is:
\[ \text{Rental Cost} = 6.50r \]

2. **Game Cost**: The cost per game is $3.75. Thus, the total cost for \( g \) games is:
\[ \text{Game Cost} = 3.75g \]

### Step 3: Calculate Total Cost Before Tax
The total cost before tax is the sum of the rental cost and the game cost:
\[ \text{Total Cost (before tax)} = 6.50r + 3.75g \]

### Step 4: Include Sales Tax
The sales tax is 6.325%. To include this in our total cost, we multiply the total cost by \( 1 + \frac{6.325}{100} \):
\[ \text{Total Cost (after tax)} = (6.50r + 3.75g) \times 1.06325 \]

### Step 5: Determine Total Money Available
Each person in the group has $20 to spend, and there are 7 people:
\[ \text{Total Money} = 20 \times 7 = 140 \]

### Step 6: Set Up the Inequality
The total cost after tax must be less than or equal to the total money available:
\[ (6.50r + 3.75g) \times 1.06325 \leq 140 \]

### Final Inequality
Thus, the inequality that best describes the situation is:
\[ 6.50r + 3.75g \leq \frac{140}{1.06325} \]