Question 46·Easy·Linear Inequalities in One or Two Variables
A robotics team has at most 25 minutes to complete two tasks in the lab. Calibrating each sensor takes 3 minutes, and testing each motor takes 4 minutes.
Let be the number of sensors calibrated and let be the number of motors tested.
Which ordered pair could represent values that meet the time limit?
When a word problem describes a maximum or minimum total, write a linear expression for the total (here ) and translate “at most” to . Then substitute each answer choice into the expression and keep only the one that satisfies the inequality.
Hints
Turn the situation into an inequality
Total time is minutes for sensors plus minutes for motors. “At most 25” translates to .
Plug in each ordered pair
For each choice, compute and check whether the result is .
Be careful about the boundary
If the total time equals 25 exactly, it still works because “at most 25” includes 25.
Desmos Guide
Enter the inequality
In Desmos, enter .
Restrict to nonnegative values (optional)
If you want to match the context of counting tasks, also enter and .
Test the choices
Type each point, such as , as a point in Desmos and see whether it lies in the shaded solution region. The point that lies in the shaded region is the answer.
Step-by-step Explanation
Write the inequality for the time limit
Each sensor takes 3 minutes and each motor takes 4 minutes, so the total time is . The phrase “at most 25 minutes” means
Check the answer choices
Substitute each ordered pair into .
- For : , which meets .
The other choices give totals greater than 25 minutes, so they do not meet the limit.
Therefore, the correct answer is (3, 4).