Question 11·Medium·Linear Functions
A cell-phone company models a customer’s monthly bill with the function
where is the total charge, in dollars, for using gigabytes of data beyond the monthly allowance.
If Ashley’s bill last month was $165, how many gigabytes beyond the allowance did she use?
For linear function word problems, first identify what each variable and expression represents, then plug the given output value (here, the total cost) into the function and solve the resulting equation. Use inverse operations in order—undo addition or subtraction first, then undo multiplication or division. Always check your solution by substituting it back into the original function to confirm it matches the given value.
Hints
Identify what 165 represents in the function
In the function , is the total cost. Ashley’s bill is $165. How can you use that information in the equation?
Set up the equation to solve for n
Replace with and write an equation involving . What equation do you get?
Solve the two-step equation
Once you have , think about which operation undoes , and then how to undo multiplying by .
Desmos Guide
Enter the cost function
Type y = 25x + 40 into Desmos. This graphs the total bill as a function of gigabytes beyond the allowance.
Represent Ashley’s bill
Type y = 165 to graph a horizontal line showing all points where the bill is $165.
Find the data usage that matches the bill
Look at the intersection point of the two graphs. The -coordinate of this intersection is the number of gigabytes beyond the allowance that Ashley used.
Step-by-step Explanation
Translate the situation into an equation
The function gives the total bill in dollars when gigabytes are used beyond the allowance.
Ashley’s bill was $165, so plug this in for :
Isolate the term with n
Solve the equation step by step.
First, subtract from both sides to undo the :
Solve for n and interpret the result
Now divide both sides by to solve for :
So Ashley used 5 gigabytes beyond the allowance, which corresponds to choice C.