Question 133·Easy·Linear Inequalities in One or Two Variables
Alexa purchases a monthly gym membership that includes a one-time sign-up fee of $30 and costs an additional $15 for each fitness class she attends. If Alexa wants to spend no more than $120 in her first month, and she can attend only a whole number of classes, what is the maximum number of fitness classes she can take that month?
(Express the answer as an integer)
Translate the situation into a linear inequality: (fixed fee) + (rate)(quantity) \le (budget). Solve the inequality, then enforce the problem’s constraint (here, must be a whole number) by taking the greatest integer that still satisfies the inequality.
Hints
Set up the cost expression
Write an expression for the total cost as (one-time fee) + (cost per class)(number of classes).
Turn the budget into an inequality
Use “no more than $120” to write an inequality involving your total cost expression.
Remember the whole-number restriction
After solving for , take the greatest whole number that still satisfies the inequality.
Desmos Guide
Enter the cost function
In Desmos, enter to represent the total cost (in dollars) as a function of number of classes .
Add the budget line
Enter to represent the maximum allowed cost.
Find where the cost meets the budget
Use the intersection of the two lines to find the largest where .
Apply the whole-number condition
Because must be a whole number of classes, take the greatest whole number not exceeding the intersection’s -value; this gives 6 classes.
Step-by-step Explanation
Define the variable and total cost
Let be the number of fitness classes Alexa attends in her first month.
The total cost (in dollars) is
Write and solve the inequality
Alexa wants to spend no more than $120, so
Subtract from both sides:
Divide by :
Use the whole-number constraint
Because must be a whole number of classes and , the greatest possible value is 6.