a company has a $150 budget to provide lunch for its 20 employees. the options are to provide either roast…

a company has a $150 budget to provide lunch for its 20 employees. the options are to provide either roast beef sandwiches, which cost $5 apiece, or tuna sandwiches, which also cost $5 apiece. the company also wants to use the entire budget. suppose r represents the number of roast beef sandwiches it provides and t represents the number of tuna sandwiches. which statement is correct? the company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r - t = 20 and 5r + 5t = 150. the company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r + t = 20 and 5r + 5t = 150. the company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r - t = 20 and 5r + 5t = 150. the company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r + t = 20 and 5r + 5t = 150.

a company has a $150 budget to provide lunch for its 20 employees. the options are to provide either roast beef sandwiches, which cost $5 apiece, or tuna sandwiches, which also cost $5 apiece. the company also wants to use the entire budget. suppose r represents the number of roast beef sandwiches it provides and t represents the number of tuna sandwiches. which statement is correct? the company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r - t = 20 and 5r + 5t = 150. the company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r + t = 20 and 5r + 5t = 150. the company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r - t = 20 and 5r + 5t = 150. the company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r + t = 20 and 5r + 5t = 150.

Answer

Explanation:

Step1: Establecer el sistema de ecuaciones

El número total de empleados es 20, entonces $r + t=20$. El presupuesto es de 150 dólares y cada sandwich cuesta 5 dólares, entonces $5r + 5t=150$.

Step2: Simplificar la segunda ecuación

Dividir la ecuación $5r + 5t=150$ entre 5, obtenemos $r + t = 30$.

Step3: Analizar el sistema

Tenemos el sistema $\begin{cases}r + t=20\r + t=30\end{cases}$. Dos ecuaciones $r + t$ no pueden ser iguales a dos valores diferentes simultáneamente, por lo que no hay solución.

Answer:

The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations $r + t=20$ and $5r + 5t=150$.