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:
The given information says that the total amount of lunch bought should equal $150 when both options cost $5:
[tex]5r+5t=150[/tex]
It also says that the food should feed all 20 employees:
[tex]r+t=20[/tex]
This is now a system. Solve by substitution.
Solve the second equation for r. Use inverse operations to isolate the variable by subtracting t from both sides:
[tex]r+t-t=20-t\\\\r=20-t[/tex]
Now insert this value of r into the first equation:
[tex]5(20-t)+5t=150[/tex]
Simplify the equation. Use the distributive property:
[tex]5(20)+5(-t)+5t=150\\\\100-5t+5t=150[/tex]
Cancel the terms:
[tex]100\neq 150[/tex]
100 does not equal 150, so there is no solution to the system.
:Done