Is there a difference for discount per unit and discount per purchase total?

Question

I can't find relevant tags for my question so I wonder if this is a good place to ask.

I wanted to ask this a long time ago but keep forgetting.

Let's suppose when shopping for 3 units of specific good with same price, I am being offered one of the following:

A) Get 20% off per unit
B) Get 20% for total purchase

Now let's suppose each unit's price is different while all else stays the same. Would that change anything?

Can you enlighten please?

Answer 1

Suppose $p_i$ is the price of the $i^{th}$ item in your shopping cart and that you purchase $n$ items. If we get $20\%$ of each item individually, then we will pay $$(1-0.2)p_1+(1-0.2)p_2+\cdots+(1-0.2)p_n.$$ We can factor out $1-0.2=0.8$ to give $$0.8(p_1+p_2+\cdots+p_n).$$ If we now examine the second equation, we have summed up all of the items and then applied our discount of $20\%$ showing that both scenarios are equivalent.

Answer 2

You are looking for the distributive property!