A linear cost model adds a fixed fee to a charge that repeats for each item. The words “for each” signal that the rate multiplies the count; the fixed fee is added only once. Write an equation for the total, then use a Desmos regression to find the count. Don’t divide the whole bill by the per-text rate, because the bill includes the fixed fee.
Hints
- Hint 1
A per-text rate means the same charge applies to every message. If is the number of texts, multiply the rate by to find the text-message charge.
- Hint 2
A fixed fee is paid once, regardless of how many texts Elena sends. Add it to the text-message charge, then set that sum equal to the total bill.
Step-by-step
Model the bill and solve in Desmos
Step 1Write the charge that repeats
Let be the number of texts. The rate applies to each text, so texts cost dollars. Multiply the repeating charge, not the fixed fee.
- Step 2
Match the charges to the total
Add the $49.99 monthly fee once, then set the sum equal to the $64.39 total:
- Step 3
Find the number of texts
Type in Desmos. The is the unknown count, and asks Desmos to find the value that makes both sides match. Under PARAMETERS, Desmos shows . So Elena sent 96 text messages. Choice C.