[Linear Algebra] - Resolving a system

[Tosh5457]

Homework Statement

Three truck drivers went into a roadside cafe. One truck driver purchased four sandwiches, a cup of coffee and ten doughnuts for $8.45. Another drivers purchased three sandwiches, a cup of coffee and seven doughnuts for $6.3. What did the third truck driver pay for a sandwich, a cup of coffee and a doughnut?

Homework Equations

The Attempt at a Solution

The system's equations are:
4s + 1c + 10d = 8.45
3s + 1c + 7d = 6.3
1s + 1c + 1d = a

The system has infinite solutions, right? There are 4 variables for 3 equations. I can't determine a.

 

[hotvette]

I don't think 'a' is intended to be a variable. I believe the objective is to solve for x,y, z in terms of 'a'. Thus, 3 equations and 3 unknowns.

 

[Tosh5457]

I don't think 'a' is intended to be a variable. I believe the objective is to solve for x,y, z in terms of 'a'. Thus, 3 equations and 3 unknowns.

I wrote the problem wrongly on the first time, I just edited it.