A total of 1185 was spent on 36 pairs of slacks. Some were dress slacks costing 40 each, and t

step 1 So we have two unknowns. The number of dress slacks and the number of casual slacks that the per

A total of 1185 was spent on 36 pairs of slacks. Some were...

Key Concepts

Word Problem Translation

This involves converting a real-world scenario described in words into a mathematical model. The process requires identifying unknown quantities, defining variables, and setting up equations based on the relationships and constraints provided in the problem statement.

System of Linear Equations

A system of linear equations consists of two or more equations with multiple variables, where the goal is to find the values of these variables that satisfy all equations simultaneously. In contexts like cost analysis or inventory management, such systems allow for a precise representation of complex relationships between different quantities.

Methods of Solving Systems (Substitution and Elimination)

The substitution and elimination methods are standard techniques for solving systems of linear equations. The substitution method involves solving one equation for one variable and then replacing that variable in another equation, while the elimination method involves combining equations to cancel out one of the variables. Both methods aim to simplify the system to find the unique solution that satisfies all given conditions.

Integer Constraints in Problem Solving

Many real-world problems, especially those involving counts of items or discrete objects, require solutions to be integers. This concept acknowledges that fractional or non-integer solutions are not acceptable in contexts where only whole numbers make sense, such as the number of purchased items.