Question

Ranch High School hosted a basketball tournament to raise money to update the school's gym. The cost for all the necessary supplies was $375. The school decided to sell adult tickets for $8.50 and child tickets for $5.00.

a. At the end of the tournament, Ranch High School determined that they sold 205 adult tickets and 125 child tickets. In order to update the school's gym, Ranch High School needs $3,500. Complete the register to determine if the school has enough money to update the gym.

b. Write an algebraic expression to represent the profit earned from the basketball tournament. Let a represent the number of adult tickets sold, and let c represent the number of child tickets sold. (Profit is the amount of money collected in ticket sales minus the cost of supplies.)

Answer 1

Ranch High School earned a total of $2367.50 from ticket sales during the basketball tournament. After subtracting the cost of supplies ($375), their profit was $1992.50, which is not enough to meet their goal of $3,500 for updating the gym. The algebraic expression for the profit earned is Profit = 8.5a + 5c - 375.

Step-by-step explanation:

To determine if Ranch High School has enough money to update the gym after the basketball tournament, we need to calculate the total revenue from ticket sales and then subtract the cost of the supplies.

The total revenue from adult ticket sales is 205 tickets × $8.50 per ticket, and from child ticket sales is 125 tickets × $5.00 per ticket. Adding these together gives us the total revenue from ticket sales.

Total Revenue from Adults = 205 × $8.50 = $1742.50
Total Revenue from Children = 125 × $5.00 = $625.00
Total Revenue = $1742.50 + $625.00 = $2367.50

Now we subtract the cost of supplies from the total revenue to find out if they have enough money to meet their $3,500 goal.

Profit = Total Revenue - Cost of Supplies
Profit = $2367.50 - $375 = $1992.50

Since the profit of $1992.50 is less than the needed amount of $3,500, the school does not have enough money to update the gym.

Next, the algebraic expression to represent the profit earned from the basketball tournament, with a representing the number of adult tickets sold and c representing the number of child tickets sold, will be:
Profit = 8.5a + 5c - 375