We can solve 3 variable systems of equations by various algebraical methods such as substitution, elimination, graphing or more.
To solve a word problem with 3 variables follow the below steps:
First read the given problem carefully and note what is given and what is required.
Denote the unknown by the variables as x, y and z (choose anything).
Translate the problem to the language of Mathematics statements.
Form the linear equations in 3 variables using the conditions given in the problems.
Solve the system of linear equations and get your result.