A mail-order lacrosse equipment business shipped 120...

A mail-order lacrosse equipment business shipped 120 packages one day. Customers are charged $\$ 3.50$ for each standard-delivery package and $\$ 7.50$ for each express-delivery package. Total shipping charges for the day were $\$ 596 .$ How many of each kind of package were shipped?

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Key Concepts

Translating Word Problems Into Equations

This concept involves reading a descriptive scenario and identifying the quantities and relationships described in words, then converting those into algebraic equations. It is crucial for breaking down a real-world problem into manageable mathematical expressions.

System of Linear Equations

A system of linear equations consists of two or more equations that share variables. Solving such a system means finding the values of these variables that satisfy all the equations simultaneously. This is a fundamental technique in algebra used to model and solve problems involving multiple constraints.

Elimination and Substitution Methods

These are methods used to solve systems of linear equations. The substitution method involves solving one equation for one variable and substituting that expression into the other equation(s). The elimination method involves adding or subtracting equations to cancel out one variable, making it easier to solve for the remaining one. Both methods are powerful tools for obtaining the solution to simultaneous linear equations.

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