# Math Help - Determing the ratio of buyers who take up a multi-buy offer (i.e. redemption rate)

1. ## Determing the ratio of buyers who take up a multi-buy offer (i.e. redemption rate)

Hi,

My question is how do i dtermine the % of shoppers who took up a multi buy offer.

So for example the product normally retails for $4.60 and the offer was buy 2 for$6.00 so if EVERYONE takes up the offer the sell price will be $2.99 right? But not everyone takes up the offer (some ppl prefer to just buy the one unit instead of two). In my data the average sell price for the week of the multi-buy promotion was$3.86

So how do i figure out the % of sales that were made were shoppers took up the multi-buy?

Thanks!

2. ## Re: Determing the ratio of buyers who take up a multi-buy offer (i.e. redemption rate

Originally Posted by agerrrard
Hi,

My question is how do i dtermine the % of shoppers who took up a multi buy offer.

So for example the product normally retails for $4.60 and the offer was buy 2 for$6.00 so if EVERYONE takes up the offer the sell price will be $2.99 right? no$3.00

But not everyone takes up the offer (some ppl prefer to just buy the one unit instead of two). In my data the average sell price for the week of the multi-buy promotion was \$3.86

So how do i figure out the % of sales that were made were shoppers took up the multi-buy?

Thanks!
Let $m$ be the fraction of your $N$ customers that took the multi-buy. Then the total sales were $m\times N\times 2+(1-m)\times N$ and the total they paid was $m\times N \times 2 \times 3.00 + (1-m)\times N \times 4.60$.

So the average price was the total received divided by the total sales:

$p=\frac{m\times N \times 2 \times 3.00 + (1-m)\times N \times 4.60}{m\times N\times 2+(1-m)\times N}$

Now the $N$s cancel and we are told that the average price paid was $\3.86$ so:

$p=\frac{m \times 2 \times 3.00 + (1-m) \times 4.60}{m\times 2+(1-m)}=3.86$

which you now solve for the (decimal) fraction of customers who took up the multi-buy, and multiply that by $100$ to get the percentage.

CB