Question 95·Medium·Linear Inequalities in One or Two Variables
A muralist is choosing jars of two paint colors for a wall.
- Each jar of Color A covers square meter.
- Each jar of Color B covers square meter.
The muralist needs to cover at least square meters. Let be the number of jars of Color A and let be the number of jars of Color B.
Which inequality represents this situation?
Translate the context directly into an inequality by adding each variable’s contribution. Use keywords (“at least” , “at most” ), then multiply by a common denominator to clear fractions so you can match a clean, simplified answer choice.
Hints
Add the two area contributions
Write the total covered area as (area per jar of A) plus (area per jar of B).
Translate the phrase
The phrase “at least” means you should use .
Remove the fractions
Multiply both sides of the inequality by the least common multiple of and to clear denominators.
Desmos Guide
Enter the inequality
In Desmos, enter .
Convert to integer coefficients (optional)
Also enter and notice it shades the same region as the original inequality.
Confirm the meaning
Check that points in the shaded region correspond to combinations that cover at least square meters (for example, try a point with larger and/or values).
Step-by-step Explanation
Write an inequality for the total area
Color A contributes square meters and Color B contributes square meters, so the total is
“At least ” means
Clear fractions
Multiply both sides by :
which simplifies to
Therefore, the correct inequality is .