ACT Math · Function notation and transformations

A library charges a late fee of $0.25 for each day or partial day a book is overdue. What is the fee for a book that is 4.2 days overdue?

A library charges a late fee of $0.25 for each day or partial day a book is overdue. What is the fee for a book that is 4.2 days overdue?

Answer and explanation

Answer: H: $1.25

Each day or partial day counts as a full day, so 4.24.2 days is billed as 55 days. The fee is 5⋅0.25=1.255\cdot0.25=1.25 dollars, choice H. Choice F ($1.05) multiplies the rate by the exact 4.24.2 days, which ignores the rounding rule. Choice G ($1.20) bills 4.84.8 days, a wrong amount. Choice J ($1.50) bills 66 days. This kind of pricing is a step function, and any fraction of a day moves the bill up to the next whole day.

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