About understanding an inequality

[srayan]

Hello.
I was solving this math problem today where i got stuck.
let, S be the number of swings made
L be the number of slides made
If the condition is the market requires that at least 2 slides be made for every swing made and I have to form an inequality based on this,
Should the inequality not be S>=2L?
I put it on the lingo model to solve and it did not work.
But then when i changed this inequality to L>=2S, then number of swings value was 10 and slides value was 20 and the equation met the requirements and got solved. I don’t understand.

 

[Dr.Peterson]

the market requires that at least 2 slides be made for every swing made

This sort of statement can be tricky to interpret. I often modify it step by step until it becomes clear:

The number of slides must be 2 times the number of swings made.​

Does that look like it means the same thing? If so, what inequality would you write? If not, how would you modify it?

 

[srayan]

I would prolly write 2L>=S or 2L<=S. I don’t really know. But it seems to me the statement you provided is the same as for one swing 2 slides have to be made.

 

[Otis]

at least 2 slides [for] every swing

Should the inequality not be S>=2L?

Hi srayan. As there are two or more slides for every swing, there must be more slides than swings. Your inequality above states the opposite (it says the number of swings is greater than the number of slides).

The inequality L ≥ 2S says the number of slides is twice the number of swings OR is greater than that.

(Not that it matters, but the given scenario seems backwards to me. Playgrounds I've seen always have more swings than slides.)
[imath]\;[/imath]

 

[Dr.Peterson]

Dr. Peterson may have forgotten to include the phrase "at least", above.

I may have forgotten, or I may have left that for @srayan to notice and correct. I'm not sure ... but there's a reason I asked a question.

I would probably write 2L>=S or 2L<=S. I don’t really know. But it seems to me the statement you provided is the same as for one swing 2 slides have to be made.

So, correcting my statement to

The number of slides must be at least 2 times the number of swings,​

do you see that this means L (the number of slides) is greater than or equal to 2S (twice the number of swings)?

A lot of the trouble here is reading the English very carefully, because it does often feel a little backwards at first.