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This would be considered a breach of contract, since they failed to perform what they contracted with you to perform. They are liable to reimburse you for the money you paid for installation. If the manager is offering to pay for installation, they are offering to settle the breach of contract.
As far as misrepresentation, if the company they sent was not licensed in your county to install, that would have made it illegal for them to do and if you file a complaint with the Attorney General's Office of Consumer Protection, if the store proves they paid you for the installation then the AG will find the matter has been settled. Furthermore, they still did deliver the drier to you and if they are giving you the $200 for installation, or $220, then you are still getting the drier for what you agreed to pay. To go to court over this, because it is breach of contract, the only damages you could get would be actual damages, no other damages and again, they are paying you for the installation as you said they have a check ready for you for that purpose and as such they are making good on the deal they made with you.
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