Final answer:
By subtracting the one-time late fee of $10 from the total penalty of $42, and dividing the remainder by the daily late fee of $5, Jane was found to be late for work six times last month, based on the payment penalties.
Step-by-step explanation:
To determine how many times Jane was late for work, we need to consider the penalties she paid last month. According to the given information, the credit card company charges a $10 fee when a payment is late and an additional $5 a day each day the payment remains unpaid. If Jane paid a total of $42 for the penalty last month, we need to calculate how many times this penalty was incurred and hence, how many times she was late.
The one-time late fee is $10, so if we subtract this amount from the total penalty of $42, we get $32 (which is $42 - $10). This remaining amount should be a multiple of the daily late fee of $5. Therefore, we divide $32 by $5 to get the number of days the payment remained unpaid, which is $32 / $5 = 6.4 days. Since the number of days cannot be in fractions and the daily charges are applied in whole days, we can infer that Jane was late for work six times last month and the remaining $2 could not represent a full late day, suggesting a possible error in the initial assumption.