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?

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.
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.
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.
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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Answer 1

2. 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.

Explanation:

The total lunch budget of the company = $150

Total number of employees = 20

The cost of 1 roast beef sandwich = $5

The cost of 1 tuna sandwich = $5

r represents the number of roast beef sandwiches provided.

t represents the number of tuna sandwiches provided.

Now, consider the given statements:

Here, total number of sandwiches purchased = Total number of employees

⇒ r + t = 20 .... (1)

Also, as each type of sandwich costs $5.

So, the cost of r roast beef sandwiches = r x ( Cost of 1 beef sandwich)

= r x ( $5) = 5 r

And, the cost of t tuna sandwiches = t x ( Cost of 1 tuna sandwich)

= t x ( $5) = 5 t

Total cost of (r +t) sandwiches = Total Lunch Budget

⇒ 5 r + 5 t = 150 .... (2)

Hence, from (1) and (2) the above situation can be represented as:

r + t = 20

5 r + 5 t = 150

Hence, 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.