Mail-Order Business. A mail-order gardening equipment...

Mail-Order Business. A mail-order gardening equipment business shipped 120 packages one day. Customers are charged $6.50$ for each standarddelivery package and $10.00$ for each express-delivery package. Total shipping charges for the day were $4$ How many of each kind of package were shipped?

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Key Concepts

System of Linear Equations

This concept involves setting up and solving two or more equations that contain the same set of variables. In problems like these, each equation represents a distinct condition or constraint, and the solution is the set of variable values that satisfy all equations simultaneously.

Translation of Word Problems into Equations

This is the process of converting a descriptive problem statement into a set of mathematical expressions or equations. It requires identifying the unknown quantities, understanding the relationships between them, and representing these relationships algebraically.

Variable Representation

This key concept refers to the use of symbols, typically letters, to denote unknown quantities in a problem. Assigning variables appropriately allows one to formulate equations that capture the essential relationships in the problem.

Diophantine Equations

In some word problems, particularly those involving counts of items, the solutions must be integers. Diophantine equations are algebraic equations for which only integer solutions are sought, reflecting the practical constraints of the problem.

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