Question

At a restaurant, you eat 2 taco salads and drink two glasses of ice tea. Your friend eats 1 taco salad and drinks 1 glass of ice tea. The restaurant charges you $11 and your friend $6.50. Can you determine the prices of taco salads and ice tea? Explain.

Answer 1

Set up a system of equations that represent x as taco salads and y as iced tea:
2x + 2y = 11 (you)
x + y = 6.50 (your friend)
Solve the system of equations by solving one of the equations for a variable:
x+y = 6.50 (I solved for y):
y = 6.50 - x.
Plug this equation into the y of the first equation:
2x + 2(6.50 - x) = 11
Solve for x:
2x + 13 - 2x = 11
2x cancels out:
13 = 11
No solution, so it is not possible to determine the prices of the items.