Question

1. members of a lacrosse team raised $1355 to go to a tournament. they rented a bus for $898.50 and budgeted $20.75 per player for meals. write and solve an equation which can be used to determine p, the number of players the team can bring to the tournament.
2. write the equation of the line in fully simplified slope - intercept form.

Explanation:

Problem 19

Step1: Define the equation

The total money raised is equal to the bus rental cost plus the total meal cost for \( p \) players. The bus rental is \(\$898.50\) and the meal cost per player is \(\$20.75\), so the equation is \( 898.50 + 20.75p = 1355 \).

Step2: Subtract 898.50 from both sides

Subtract \( 898.50 \) from each side to isolate the term with \( p \): \( 20.75p = 1355 - 898.50 \). Calculate the right side: \( 1355 - 898.50 = 456.5 \). So, \( 20.75p = 456.5 \).

Step3: Solve for \( p \)

Divide both sides by \( 20.75 \): \( p=\frac{456.5}{20.75} \). Calculate the division: \( \frac{456.5}{20.75} = 22 \).

Step1: Identify slope and intercept

The slope - intercept form of a line is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. From the graph, the line crosses the y - axis at \( (0,-9) \), so \( b=-9 \). To find the slope, we can use two points. Let's take the y - intercept \( (0, - 9) \) and another point, say \( (1,-2) \) (by looking at the grid, we can see that for a run of 1 (from \( x = 0 \) to \( x = 1 \)), the rise is \( - 2-(-9)=7 \)). Wait, let's check another pair. If we take \( (2,5) \) and \( (0,-9) \), the slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{5-(-9)}{2 - 0}=\frac{14}{2}=7 \).

Step2: Write the equation

Using the slope - intercept form \( y=mx + b \) with \( m = 7 \) and \( b=-9 \), the equation is \( y = 7x-9 \).

Answer:

The equation is \( 898.50 + 20.75p = 1355 \) and the number of players \( p = 22 \).

Problem 20