A company has a 150 dollars budget to provide lunch for its 20 employees. The options are to provide either roast beef sandwiches, which cost 5 dollars apiece, or tuna sandwiches, which also cost 5 dollars 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?
Answer
A
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 plus t is equal to 20 and 5 r plus 5 t is equal to 150 .
B
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 minus t is equal to 20 and 5 r plus 5 t is equal to 150 .
C
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 plus t is equal to 20 and 5 r plus 5 t is equal to 150 .
D
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 minus t is equal to 20 and 5 r plus 5 t is equal to 150 .
Explanation
Feeding all 20 employees requires r + t = 20, while spending the full $150 requires 5r + 5t = 150. Dividing the cost equation by 5 gives r + t = 30, which contradicts r + t = 20. So there is no solution, and the company cannot meet both goals; choice C is correct.
AI-written and checked against the verified answer.