A two-variable inequality models a total that depends on two counts and must meet a limit. Multiply each rate by its matching count, then add the amounts. For a minimum, the total can equal the target or exceed it; using a less-than sign would describe a maximum instead.
Hints
- Hint 1
A unit rate is the pay for one package. Multiply the small-package rate by and the large-package rate by . How can you add those amounts without swapping the rates?
- Hint 2
An inclusive minimum allows Oscar to earn exactly the target as well as more. At least is not an upper limit. Which inequality sign includes both an exact match and any amount above it?
Step-by-step
Build the earnings inequality
Step 1Write Oscar’s total pay
No Desmos needed. You’re translating the pay rule, not solving a given expression. Each of the small packages pays $4, giving . Each of the large packages pays $6, giving . Add the two kinds of pay:
- Step 2
Apply the minimum Oscar wants
Oscar wants at least $100. That includes earning exactly $100 or earning more. “At least” means greater than or equal to, not less than or equal to. So his total pay must satisfy . This says Oscar earns $100 or more from the packages. Choice D.