Christmas Grocery hours

Algebra Level 2

In Australia, shops are required to remain closed on Christmas day, December 25. (They are also closed Good Friday, but that is irrelevant to this problem).

The grocery store that I go to is open from 10am to 8pm every weekday, and 8am to 10pm every weekend.

From December 22 to 28 in 2013 (inclusive), how many hours is the grocery shop open for?


The answer is 68.

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11 solutions

Sowmya Km
Dec 16, 2013

22nd & 28th are weekends. so it comes to 28 hrs. ( from 8am - 10 pm) 25th holiday. rest 4 days 10 hrs each . = > 28 +40 = 68 hrs

Alix Buttimore
Dec 16, 2013

The 22nd is a Sunday; the 28th a Saturday. We're looking at a period of 8 days. Two of these days are weekend days, five are weekdays but Christmas doesn't count, so that makes four. On a weekday, the store is open from 10am to 8pm which is 12 hours minus 2, 10 hours. On the weekend, the store is open from 8am to 10pm which is 12 hours plus two, 14. The total amount of hours is consequently 4 10 + 2 14 = 40 + 28 = 68 4*10+2*14=40+28=68 .

Husnain Raza
Dec 16, 2013

22-sunday=14hrs 23-monday=10hrs 24-tuesday=10hrs 25-wednesday=0hrs 26-thursday=10hrs 27-friday=10hrs 28-saturday=14hrs so total hrs are 68

From 10am to 8pm each weekday is 10 hours. So (10 hrs/day)(4 days) = 40 hours. Remember, Christmas does NOT count (it's on a Wednesday). From 8am-10pm each weekend is 14 hours, so (14 hrs/day)(2 days) = 28 hours. In total, 40 hours + 28 hours = 68 hours.

Khaled Mohamed
Feb 12, 2014

weekdays ( 5days ) from 10 am ---> 8 pm ( 10 hours )

weekends ( 2days ) from 8 am -----> 10 pm ( 14 hours )

Let: Dec 22 , 23 , 24 ,25 , 26 , 27 . 28 be: Sat, Sun, Mon, Tues, Wed, Thurs, Fri in this sequence

as we exclude Tuesday ( December 25 is closed)

then the total hours equals: 2(14) + 4(10) = 68 hours

Joshua del Mar
Jan 21, 2014

let x = total hours of grocery shop open... time open on weekdays =10am - 8pm =10hours... time open on weekends =8am -10pm = 14hours... we can put dec. 25 as = -hours.. but first we need to determine if it is weekend or weekday.. so you need to look for calendar on 2013.. and it is on Wednesday.. now since there are 5weekdays and 2 week ends.. we can say 10(5-1) + 14(2)= x... 40+28=x.. 68=x...

Ricky K
Jan 8, 2014

Grocery store -

weekday -> 5 days -> mon-fri weekend -> 2 days -> sat-sun

weekday -> 10:00->20:00 = 10 hours weekend -> 08:00->22:00 = 14 hours

(see your calendar) weekend from 22 to 28 -> 2 days weekdays from 22 to 28 = 4 days holiday = 25 (Does not count)

(2x14)+(4x10) = 28 + 40 = 68

Ryan Soedjak
Dec 28, 2013

This is a horrible problem because it only is valid for years that 25th dec is on a weekday.

Sean Roberson
Dec 16, 2013

Rewrite the times using military time/24-hour time: that is, 1000 to 2000 during the week, and 0800 to 2200 on the weekends. It will be open for 10 hours during the week and 14 on the weekends. The week in question includes a Saturday, Sunday, and four open days in the week. So, the store will be open 2 ( 14 ) + 4 ( 10 ) = 68 2(14)+4(10) = \boxed{68} hours this week.

Kacper Kazaniecki
Dec 16, 2013

on week days shops are open from 10am to 8 pm which is 10 hours. and on weekends they are open from 8am to 10pm which is 14 hours so from 22nd to 28th is 7 days , ( 2 weekend days and 5 week days ) also we know that shops are closed on the 25th which is on Wednesday which leaves us with 4 weekdays and 2 weekend days. as I said before a weekday is 10 hours and a weekend day is 14 hourse. So we do (14 * 2 ) + ( 10 * 4 ) which is 68

Kshitij Johary
Dec 16, 2013

There are 7 days between December 22 to December 28 (inclusive) but since we are given that the shop is closed on Christmas, 6 days remain with us. As there are 7 days, there must be a Saturday,Sunday and 4 weekdays (excluding Christmas). As the shop is open for 10 hours every weekday and 14 hours every weekend, doing the appropriate calculations will lead us to an answer of 68 hours during this interval.

what if 25 dec fall on weekend?

gagandeep singh bhatia - 7 years, 5 months ago

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Ah, I wrote the problem with this year in mind. I should ask them to make an edit to reflect that.

Sorry about the oversight!

Chung Kevin - 7 years, 5 months ago

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luckily i dont know thr r 2 dayz of weekend :(

Mohammad Oli Al Islam - 7 years, 5 months ago

25 Dec 2013 mentioned in the ques. is Wednesday.

Pankaj Joshi - 7 years, 5 months ago

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