Does Google Rank Pages For Multiple Keywords

[justcurious]

Hi all,

I am running an ecommerce website and I am obviously trying to get on the first page of SERP for my products.

With a lot of luck and just as much hard work, I have achieved first page success for the keywords "Cheap Products" and "Budget Products" which is great, but the number of monthly searches for these keywords is in the low hundreds, whereas the number of monthly searches for "Products" is around 12k. "Products" is currently coming in at position 31/32 (page 4) which of course means it might just as well be at position 100 to all intents and purposes.

There is a fair amount of reference on the page to "Best Value", "Great Value" and "Lowest Prices" which has presumably worked in my favour for the lower search count keywords.

My question is, are the references to "Best Value", "Great Value" and "Lowest Prices" hurting my ranking for the keyword "Products" and should I remove them, or will removing them make no difference at all (other than lose my position for "Cheap Products").

Any insights or recommendations would be much appreciated.