City regulations limit food truck operators to no more than 48 hours of operation per week. Aria’s food truck has already been open for 33 hours this week. What is the greatest number of additional hours Aria can operate the truck this week without violating the regulations?
A weekly cap gives an inequality, a statement that allows a range of values. Add the time already used to the extra time, and keep that total at or below the limit. Subtract the used time to find the greatest extra time. The trap is treating the weekly limit as if it were all still available.
Hints
- Hint 1
The limit applies to the truck’s total hours this week, not only the hours Aria can add. If is the number of additional hours, what expression gives the total?
- Hint 2
The words no more than mean the total can equal the limit but cannot exceed it. Write an inequality for the total, then subtract the hours already used.
Step-by-step
Subtract from the weekly limit
Step 1Write the limit on total hours
No Desmos needed. Finding the remaining hours takes one subtraction. Let be the additional hours. Aria has already operated for hours, so her total would be . The 48-hour cap applies to that total, not to the additional hours alone. “No more than” includes , so write the inequality:
- Step 2
Isolate the additional hours
Subtract from both sides; subtracting keeps the inequality sign pointing the same way:
- Step 3
Interpret the boundary
Calculate the remaining hours:
The symbol includes its boundary, so 15 additional hours is allowed. Any more would put Aria over the weekly limit. The greatest number of additional hours she can operate is . Choice D.