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

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?

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## migrated from mathematica.stackexchange.comJun 6 at 21:12

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Mathematica != Mathematics. But if one buys 2 unit at 10€ each with 20% on each one would pay 2*8€. If one buys 2 units and gets 20% on 20€ one would pay 16€. –  Öskå Jun 6 at 17:16
This question appears to be off-topic because it is not about Mathematica –  Michael E2 Jun 6 at 20:54
@Öskå Hi, can you take a look on my updated question? –  Boris_yo Jun 8 at 3:26

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.