A two-variable inequality describes which combinations meet a limit. Multiply each color’s coverage per jar by its jar count, then add the amounts. The words at least tell you which inequality sign to use, while the supplied graph confirms that the line itself counts. Clear fractions on both sides before matching a choice.
Hints
- Hint 1
The total coverage comes from both colors together. Multiply each color’s area per jar by its number of jars, then add. What expression measures the whole painted area?
- Hint 2
At least means the muralist can cover exactly the required area or more. Which inequality sign includes equality and points toward larger amounts?
- Hint 3
To compare your inequality with the choices, clear the fractions. Multiplying by a positive number keeps the inequality sign facing the same way, but you must multiply both sides.
Step-by-step
Build the coverage inequality
Step 1Express the total coverage
No Desmos needed. The figure already shows the shading, and the jar rates give the total directly. Each A jar covers square meter, so jars cover . Similarly, jars of B cover . Add the two colors to get the total:
- Step 2
Translate the minimum area
The muralist needs at least square meters, so the total must be greater than or equal to :
The figure’s solid line includes combinations that cover exactly square meters; its shading is on the side with greater coverage.
- Step 3
Clear the fractions
Multiply both sides by to clear the fractions. Multiplying by a positive number keeps the inequality sign facing the same way. Write the multiplication:
Simplify both sides:
This inequality represents jar combinations that cover at least square meters. Choice A.