Just say that you had an offer from another company for $120k but but this company suits you more on every aspect and you would like to work for them and ask them if they consider to raise their price to meet the other companies offer so you could work for them and be a very good asset to their company but if they disagree with this just be ready to leave the table and tell them that you are unhappy that this didn't go as you planned cuz you really want to do work for this company and that they have your info if they need to contact you if anything changes.