Question

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?
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 minus t = 20 and 5 r + 5 t = 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 + t = 20 and 5 r + 5 t = 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 minus t = 20 and 5 r + 5 t = 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 + t = 20 and 5 r + 5 t = 150.

Answer 1

SOLUTION

TO DETERMINE

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?

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 - t = 20 and 5 r + 5 t = 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 + t = 20 and 5 r + 5 t = 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 - t = 20 and 5 r + 5 t = 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 + t = 20 and 5 r + 5 t = 150.

EVALUATION

Here it is given that , the company has a $150 budget to provide lunch for its 20 employees.

Now r represents the number of roast beef sandwiches it provides and t represents the number of tuna sandwiches.

So by the given condition

$\sf{r + t = 20 \: \: \: - - - (1)}$

The options are to provide either roast beef sandwiches, which cost $5 apiece, or tuna sandwiches, which also cost $5 apiece.

Also the company also wants to use the entire budget.

So by the given condition

$\sf{5r + 5t = 150 \: \: \: - - - - - (2)}$

Which can be simplified to

$\sf{r + t = 30 \: \: \: - - - (3)}$

Now Equation 1 and Equation 3 has no solution

Therefore 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 5 r + 5 t = 150.

FINAL ANSWER

Hence the correct option is :

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 + t = 20 and 5 r + 5 t = 150.

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