A bill with a fee paid once and a price “for each” item calls for a linear equation: fixed fee plus rate times count equals total. Multiply the per-item rate by the count, but add the fixed fee once. Translate the bill, then use a Desmos regression to find the count. Subtracting the fee alone gives a dollar amount, not a number of items.
Hints
- Hint 1
A unit rate is a charge for one item. The words for each text message tell you to multiply the price per message by the number sent. What expression gives the total charge for texts?
- Hint 2
A fixed fee stays the same no matter how many texts are sent. Add it once to the text charges. What equation makes that sum equal the whole bill?
Step-by-step
Model the bill and solve in Desmos
Step 1Write the charge for texts
Let count the text messages. The unit rate, or cost for one message, is $0.15 per message, so messages cost dollars. This is the part of the bill that changes with the message count.
- Step 2
Build the bill equation
The fixed fee of $25 is paid once, so add it to the text charges. The total bill is $46, giving . Don’t multiply by ; that would charge the monthly fee for every message.
- Step 3
Find the message count
Type as a regression. Use instead of so Desmos finds a number rather than graphs ; tells it to match the two sides. Under PARAMETERS, Desmos shows . Since counts messages, the customer sent 140 text messages. Grid in 140.