Final answer:
After calculating the number of minutes represented by the $81.78 charge, it's confirmed that Amy's least phone service charge, according to the given model, could be $81.78 if she used 1163 minutes in a month.
Step-by-step explanation:
The student's question is related to a linear equation representing a phone service cost model. To determine if the statement is true or false, we must calculate the number of minutes Amy used given the least amount she was charged, and then apply the cost model to check the correctness of the statement.
The cost model for Amy's phone service is a fixed monthly fee of $12 plus $0.06 per minute of use. To find out how many minutes correspond to the charge of $81.78, we need to subtract the fixed fee from the total charge and then divide by the per-minute rate.
So we have:
- Total charge - Fixed fee = $81.78 - $12 = $69.78
- Minutes used = $69.78 / $0.06
- Minutes used = 1163 minutes
Now we multiply this number of minutes by the per-minute rate and add the fixed fee to confirm:
- Total cost for minutes used = 1163 minutes * $0.06/minute = $69.78
- Total cost = Fixed fee + Cost for minutes used = $12 + $69.78 = $81.78
As the calculations confirm the total charge of $81.78, the statement that the least Amy has been charged in a month is $81.78 could be true if this is based on her usage of 1163 minutes.