The total amount raised from selling tickets at each concert is given by the equation 25t. Since the band is planning to hold multiple concerts, the total amount raised is also given by 25t * c.
We also know that for each concert, the band will have to pay $1,250 in fees. So the total amount raised after deducting the fees is given by 25t * c - 1,250c.
To reach the fundraising goal of $20,000, the inequality is:
25t * c - 1,250c ≥ 20,000
Graphing this inequality on the coordinate plane would require a 3-D graph, which is not possible to show here. However, we can rewrite the inequality to get a better understanding.
Dividing both sides of the inequality by 25:
tc - 50c ≥ 800
Factoring out c from the left side:
c(t - 50) ≥ 800
Since t and c represent the number of tickets sold and number of concerts held respectively, they must be positive integers. Therefore, we can rewrite the inequality as:
c ≥ 800 / (t - 50)
We can now graph this inequality on a 2-D graph, where t is the x-axis and c is the y-axis.
Graphing the line t = 50 as a vertical line, we can see that the inequality is undefined for t ≤ 50.
For t > 50, the inequality states that c must be greater than or equal to 800 / (t - 50). This means that as t increases, the value of c must also increase to satisfy the inequality. The graph will show a region in the first quadrant where c is greater than or equal to 800 / (t - 50) for t > 50.
Please note that without specific values for t, it is not possible to graph the inequality accurately.
22.4: Charity Concerts
A popular band is trying to raise at least $20,000 for charity by holding multiple concerts at a park. It plans to sell tickets at $25 each. For each 2-hour concert, the band would need to pay the park $1,250 in fees for security, cleaning, and traffic services.
The band needs to find the combinations of number of tickets sold, t, and number of concerts held, c, that would allow it to reach its fundraising goal.
Create an inequality and graph it on the coordinate plane.
1 answer
1 answer