Question 61·Easy·Linear Inequalities in One or Two Variables
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?
For word problems with limits like "no more than," "at most," or "no less than," first translate the phrase into an inequality (for example, total maximum). Define a variable for the unknown quantity (such as additional hours), write an expression for the total, and set it less than or equal to the limit. Then solve the simple equation or inequality—often this is just subtracting the amount already used from the maximum allowed—to find the largest value that still satisfies the condition.
Hints
Understand the phrase "no more than 48 hours"
Think about whether "no more than 48 hours" means the truck can be open less than, greater than, or equal to 48 hours in total.
Represent the unknown with a variable
Let be the number of additional hours Aria can still operate. How can you write an expression for the total hours for the week using ?
Write and solve an inequality
Write an inequality that shows the total hours (hours already used plus additional hours) must not go over 48. Then solve that inequality for to find the largest possible value.
Desmos Guide
Use Desmos to compute the remaining hours
In the Desmos calculator, type 48 - 33 and press Enter. The value that appears is the greatest number of additional hours Aria can operate without going over the weekly limit.
Step-by-step Explanation
Translate the word limit into math
"No more than 48 hours" means the total hours Aria’s truck is open in a week must be at most 48. In math, if is the number of additional hours, then the total is , and it must satisfy .
Set up and solve the inequality
Start with the inequality for the total hours:
Subtract 33 from both sides:
So must be less than or equal to .
Interpret the result
Compute to find the largest whole number of additional hours that still stays within the limit. That value is the greatest number of extra hours Aria can operate this week, which matches answer choice 15.