buy-4-get-1-free math

[Shmuel]

I am trying to start a canteen and cant figure out the soda prices. I bought a 12-case for $4.59. That means that each can is worth $.3825 right? So if i charge $.50 per can with a buy-4-get-1-free policy,
1)how much money will i be making a case
and
2)after how many cases will i have paid back every single can and be left with profit(meaning i can only sell 8 cans with 2 free in one case, so i am left with 2 sodas from one case and 2 sodas from the next case to make 4 to give away a free one. when will it result in a full 12-pack case, and how much money will i have spent on cases and made in total?)

 

[Deleted member 4993]

I am trying to start a canteen and cant figure out the soda prices. I bought a 12-case for $4.59. That means that each can is worth $.3825 right? So if i charge $.50 per can with a buy-4-get-1-free policy,
1)how much money will i be making a case
and
2)after how many cases will i have paid back every single can and be left with profit(meaning i can only sell 8 cans with 2 free in one case, so i am left with 2 sodas from one case and 2 sodas from the next case to make 4 to give away a free one. when will it result in a full 12-pack case, and how much money will i have spent on cases and made in total?)

Each can will make $(.5 - .3825 =) profit.

Continue....

 

[stapel]

I am trying to start a canteen and cant figure out the soda prices. I bought a 12-case for $4.59. That means that each can is worth $.3825 right? So if i charge $.50 per can with a buy-4-get-1-free policy,

1)how much money will i be making a case, and

2)after how many cases will i have paid back every single can and be left with profit (meaning i can only sell 8 cans with 2 free in one case, so i am left with 2 sodas from one case and 2 sodas from the next case to make 4 to give away a free one. when will it result in a full 12-pack case, and how much money will i have spent on cases and made in total?)

About the "buy four, get one free" policy: Will they have a punch-card or some other tracking mechanism, so that they can keep track of their purchases, up to the fourth can? Or do they have to purchase all four at the same time, so some will be using the policy (making a purchase for themselves and four friends) and others will not (buying only for themselves, etc)?

When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!

 

[HallsofIvy]

I am trying to start a canteen and cant figure out the soda prices. I bought a 12-case for $4.59. That means that each can is worth $.3825 right? So if i charge $.50 per can with a buy-4-get-1-free policy,

4.59/12= 0.3825 is correct. With a "buy-4-get-1-free policy", that is $2.00 for 5 cans. 5 cans cost you 5(0.3825)= $1.9125 so you make a profit of $2.00- 1.9125= 0.075 (7 and 1/2 cents) per 5 cans so 0.075/5= 0.015 (1 and 1/2 cents) per can.

1)how much money will i be making a case

There are 12 cans in a case so you will make 12(0.015)= 0.18 or 18 cents per case.

and
2)after how many cases will i have paid back every single can and be left with profit(meaning i can only sell 8 cans with 2 free in one case, so i am left with 2 sodas from one case and 2 sodas from the next case to make 4 to give away a free one. when will it result in a full 12-pack case, and how much money will i have spent on cases and made in total?)

Since 5 and 12 are "mutually prime", to sell an integer number of cases as 5 can units, you will need to sell 12 cases, 60 cans. 12 cases will have cost you 12(4.59)= $55.08. Selling 60/5= 12 sets of 5 cans at $2.00 each gives you $60.00 gross profit so 60- 55.08= $4.92 net profit.
(Hardly worth the trouble!)

 

[Shmuel]

4.59/12= 0.3825 is correct. With a "buy-4-get-1-free policy", that is $2.00 for 5 cans. 5 cans cost you 5(0.3825)= $1.9125 so you make a profit of $2.00- 1.9125= 0.075 (7 and 1/2 cents) per 5 cans so 0.075/5= 0.015 (1 and 1/2 cents) per can.


There are 12 cans in a case so you will make 12(0.015)= 0.18 or 18 cents per case.



Since 5 and 12 are "mutually prime", to sell an integer number of cases as 5 can units, you will need to sell 12 cases, 60 cans. 12 cases will have cost you 12(4.59)= $55.08. Selling 60/5= 12 sets of 5 cans at $2.00 each gives you $60.00 gross profit so 60- 55.08= $4.92 net profit.
(Hardly worth the trouble!)

Thank you SOOOOOOO MUCH!!!