Question 49·Easy·Linear Inequalities in One or Two Variables
To meet her weekly fitness goal, Emma needs to exercise for at least 120 minutes this week. So far she has completed 85 minutes of exercise. What is the minimum number of additional minutes Emma must exercise to meet her goal?
For word problems about “at least” or “at most” time or quantity goals, first identify the target total and how much has already been completed. Then write a simple equation (or inequality) like “completed + additional = goal” and solve for the additional amount, usually by subtracting the completed amount from the goal. This keeps your work organized and helps you avoid common mistakes like adding instead of subtracting.
Hints
Focus on the total needed
Emma needs at least 120 minutes of exercise. If you want the minimum extra time she must exercise, what total should you aim for: more than 120 or exactly 120?
Account for what she has already done
She has already done 85 minutes. Think of an equation like “minutes already done + additional minutes = total minutes needed.” What numbers and symbol could you use to fill that in?
Solve for the additional minutes
If your equation looks like , how can you isolate ? What arithmetic operation should you use to move 85 to the other side, and what calculation does that give you?
Desmos Guide
Use Desmos to compute the remaining time
In a new expression line, type 120 - 85. The value that Desmos displays is the number of additional minutes Emma must exercise to reach her 120-minute goal.
Step-by-step Explanation
Understand the goal
The phrase “at least 120 minutes” means Emma needs a minimum total of 120 minutes of exercise this week (120 or more). To find the fewest extra minutes she needs, we consider exactly 120 minutes as the target.
Write an equation for the additional minutes
Let be the number of additional minutes Emma must exercise.
She already has 85 minutes, so her total will be . To just meet her goal (the minimum), set this equal to 120:
Now solve for by isolating it:
Calculate and answer the question
Now do the subtraction:
So . This means Emma must exercise 35 more minutes to meet her goal. The correct answer is 35.