The problem is the word "cheaper".

For the opposite word, "expensive", it all depends on the word before it: "as expensive" or "more expensive".

"100 widgets cost $100. Unit price is $1." They are now twice _as_ expensive -> they now cost $200. Unit price is now $2.

"100 widgets cost $100. Unit price is $1." They are now two times _more_ expensive -> they now cost $300. Unit price is now $3.

But How do you do this with the word "cheap"? Does "cheaper" clearly mean "3x as cheap" or "3x more cheap" (which even sounds a bit wrong)? I guess it means "more cheap" means "cheaper".

Better to avoid the problem and say "They are now two times the cost, or half the cost". Which is much clearer.

> For the opposite word, "expensive", it all depends on the word before it: "as expensive" or "more expensive".

Frustratingly, I find this isn't always true in practice. Lots of people use "x times as y" and "x times more y" interchangeably. To avoid ambiguity I try to only use the former in any context where precision is useful.

True. But people also say "percentage" when they mean "percentage points". Once they notice the difference they tend to stay right.

What would 1x cheaper mean? 100% of the original price?

That reminds of the sign "Buy one, get one". Does that mean you pay for an item and you get that item, or you pay for an item and you get another item for free? I expect the meaning to the be the second one, but my brain parses it to be the first one.

That’s because it they have left off the word “free” - it’s just an odd shortening of the less ambiguous “buy one get one free”, probably made by someone who is very familiar with seeing “buy one get one free”

It not really all that odd in retail. “BOGO” (pronounced bo-go) is quick to say on the floor and is less awkward than “BOGOF” which sounds like either a franken-portmanteau of “beef” and “stroganof [sic]” or an amateur spy’s attempt at a cover identity.

It’s also used more generally for buy one get one X% off sales and you’ll see lots of “BOGO50” promo/coupon codes. Then marketing jumped on the bandwagon and started plastering “BOGO” all over marketing material so consumers are used to the lingo now

Yes?

There’s definitely some fun math party tricks in here if we can start with 1x cheaper = 0% cheaper.