Question

Members of a softball team raised $1943.50 to go to a tournament. They rented a bus for $1148.50 and budgeted $53 per player for meals. Write and solve an equation which can be used to determine x

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x, the number of players the team can bring to the tournament.

Answer 1

The softball team can bring 15 players to the tournament.

Explanation:

We can model the situation using a linear equation in slope-intercept form, whose general equation is given by:

y = mx + b, where

• (x, y) is any point on the line,
• m is the slope (change in y / change in x),
• and b is the y-intercept (y value when x = 0)

Identifying the slope:

Since it costs $53 per player, this is the slope as cost (y) changes per each player needing a meal (x).

Identifying the y-intercept and equation representing the situation:

We know that the team pays $1148.50 for the bus and additional costs come from the number of players needing meals.

Thus, 1148.50 is the y-intercept.

Therefore, the equation modeling the situation is y = 53x + 1148.50

Solving for x:

Since the team raised $1943.50 for the tournament, we can substitute 1943.50 for y in our equation to solve for x, the number of players the team can bring to the tournament:

(1943.50 = 53x + 1148.50) - 1148.50

(795 = 53x) / 53

15 = x

Thus, the team can take no more than 15 players to the tournament, in order to not exceed their budget.