Algebra / Linear Functions
Units, rates, and contextual constraints
Contextual algebra problems often combine units, rates, initial values, and restrictions such as budgets or nonnegative amounts.
Least you need to know
- Track units to identify rates.
- Use $\le$ for maximums and budgets.
- Use $\ge 0$ when a modeled amount cannot be negative.
Key notation
- C — A total cost in dollars
- t — A time input
Worked example
A cost of $40 plus $5 per hour is $C=40+5h$. If the budget is $100$, then $40+5h\le 100$.
Common mistakes
- Rounding in context must keep the answer possible.
- A model can have a practical domain even if the expression is algebraically defined for all real numbers.
How to recognize it
- The problem includes units such as dollars, hours, miles, pages, or liters.
- The question asks for a greatest or least whole number.
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