Question

Please help!

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.

Step-by-step 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."