the drama department at a school needs to make a profit of at least $1,500 from the school play. the total…

the drama department at a school needs to make a profit of at least $1,500 from the school play. the total cost to produce the play is $5,000. the drama department sells tickets to the play for $7.50 each.\na. create an inequality to model this situation using t to represent the number of tickets sold.\nb. how many tickets must the drama department sell to make a profit of $1,500?

the drama department at a school needs to make a profit of at least $1,500 from the school play. the total cost to produce the play is $5,000. the drama department sells tickets to the play for $7.50 each.\na. create an inequality to model this situation using t to represent the number of tickets sold.\nb. how many tickets must the drama department sell to make a profit of $1,500?

Answer

Explanation:

Step1: Definir la fórmula de ganancia

La ganancia $G$ es igual al ingreso menos el costo. El ingreso es el precio por boleto ($7.50$) multiplicado por el número de boletos vendidos $t$, y el costo es $5000$. Queremos una ganancia de al menos $1500$, entonces la inecuación es $7.5t - 5000\geq1500$.

Step2: Resolver la inecuación para $t$

Agregamos $5000$ a ambos lados de la inecuación: $7.5t\geq1500 + 5000$, es decir $7.5t\geq6500$. Luego dividimos ambos lados por $7.5$: $t\geq\frac{6500}{7.5}=\frac{65000}{75}=\frac{2600}{3}\approx866.67$.

Answer:

A. $7.5t - 5000\geq1500$ B. $867$ (Debido a que no se pueden vender fracciones de boletos, redondeamos hacia arriba)