A linear inequality models a budget when you can buy different amounts of two items but can't exceed a spending limit. Multiply each item's price by the variable that counts it, then add the costs. Match each price to its variable before choosing the inequality sign. “No more than” includes spending exactly the limit.
Hints
- Hint 1
A unit price is the cost of one item. Multiply the notebook price by the number of notebooks, not by the number of pens. What expression gives the notebook cost?
- Hint 2
A budget limit puts a ceiling on total spending. Add the notebook and pen costs, then choose a symbol that allows spending less than or exactly the limit.
Step-by-step
Build the budget inequality
Step 1Find the notebook cost
No Desmos needed. The prices and budget let you write the inequality directly. Each notebook costs $4, and counts notebooks, so the notebook cost is dollars. Don't put the pen price on .
- Step 2
Find the pen cost
Each pen costs $2, and counts pens, so the pen cost is dollars.
- Step 3
Apply the spending limit
Add the two costs. No more than $120 means the total can be less than or equal to $120, so . The club can spend exactly $120, but it can't spend more. Choice D.