Question

each patron can borrow the books for 2 weeks and renew the loan twice. what is the maximum number of days can a patron keep the books he borrowed from the library?

Explanation:

Step1: Determine total borrowing periods

Each borrowing period is 2 weeks, and the patron can borrow and renew twice (so total of 1 + 2 = 3 periods? Wait, no: initial borrow is 1 time, renew twice, so total periods: 1 (original) + 2 (renews) = 3? Wait, no: "borrow for 2 weeks and renew the loan twice" – so original loan: 2 weeks, then two renewals, each also 2 weeks? Wait, the problem says "borrow the books for 2 weeks and renew the loan twice" – so each loan (original + renewals) is 2 weeks. So number of periods: 1 (original) + 2 (renewals) = 3 periods? Wait, no: when you borrow, that's one period (2 weeks), then renew twice, so each renewal is an extension of 2 weeks. So total time is (1 + 2) 2 weeks? Wait, no: original loan: 2 weeks. Then renew twice: each renewal is another 2 weeks. So total number of weeks: 2 weeks (original) + 2 2 weeks (renewals) = 2 + 4 = 6 weeks? Wait, no, maybe the initial borrow is 2 weeks, and each renewal is also 2 weeks, and you can renew twice. So total periods: 1 (borrow) + 2 (renew) = 3 periods, each 2 weeks. So total weeks: 3 2 = 6 weeks. Then convert weeks to days: 1 week = 7 days, so 6 7 = 42 days. Wait, let's check again.

Wait, the problem: "Each patron can borrow the books for 2 weeks and renew the loan twice." So "borrow for 2 weeks" – that's the initial loan period. Then "renew the loan twice" – each renewal is a new loan period of 2 weeks? Or does renew mean extending the current loan? But in library terms, usually, a renewal is an extension of the current loan, so each renewal adds 2 weeks. So initial loan: 2 weeks. First renewal: +2 weeks. Second renewal: +2 weeks. So total time: 2 + 2 + 2 = 6 weeks. Then 6 weeks * 7 days/week = 42 days.

Wait, let's structure the steps:

Step1: Calculate total number of loan periods

Original borrow: 1 period. Renewals: 2 periods. Total periods: 1 + 2 = 3 periods.

Step2: Calculate total weeks

Each period is 2 weeks. So total weeks: 3 * 2 = 6 weeks.

Step3: Convert weeks to days

1 week = 7 days. So total days: 6 * 7 = 42 days.

Answer:

42