Question

Please help!

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

Answer 1

For the linear system :

r+t = 20 and 5(r+t) = 150

If you sub in the first equation into the second, you will get: 100 = 150, which is incorrect

It means the system does NOT have solutions.

Answer will be the last choice

Answer 2

Answer: 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 5r+5t=150.

Explanation:

Let 'r' represents the number of roast beef sandwiches it provides and 't' represents the number of tuna sandwiches.

Then, the total number of roast beef sandwiches and tuna sandwiches is equal to the number of employees :

`r+t=20`....................(1)

Also, the cost of each roast beef sandwich and cost of each tuna sandwich is same as $5.

If company wants to use the entire budget of $150, then we have another equation :-

`5r+5t=150\\\5(r+t)=150`

If we divide 5 on both sides we get

`r+t=30`.............................(2)

When we compare equation (1) and (2) we get 20=30 but it is not possible therefore the system has no solution.

Therefore, the correct statement is "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."