You have to comply with the terms of the contract - a verbal notice did not comply with the terms of the contract.
However, as to the cost of the equipment - you did what the salesman told you to do. The salesman has the implied apparent authority to tell you want to do. As such, the salesman bound the alarm company to their statements.
The law of agency is an area of commercial law dealing with a contractual or quasi-contractual, or non-contractual set of relationships when a person, called the agent, is authorized to act on behalf of another (called the principal) to create a legal relationship with a third party. Succinctly, it may be referred to as the relationship between a principal and an agent whereby the principal, expressly or impliedly, authorizes the agent to work under his control and on his behalf. The agent is, thus, required to negotiate on behalf of the principal or bring him and third parties into contractual relationship. This branch of law separates and regulates the relationships between:
Agents and principals;
Agents and the third parties with whom they deal on their principals' behalf; and
Principals and the third parties when the agents purport to deal on their behalf.
The common law principle in operation is usually represented in the Latin phrase, qui facit per alium, facit per se, i.e. the one who acts through another, acts in his or her own interests and it is a parallel concept to vicarious liability and strict liability in which one person is held liable in criminal law or tort for the acts or omissions of another.
An agent who acts within the scope of authority conferred by his or her principal binds the principal in the obligations he or she creates against third parties. There are essentially three kinds of authority recognized in the law: actual authority (whether express or implied), apparent authority, and ratified authority.
Main article: Actual authority
Actual authority can be of two kinds. Either the principal may have expressly conferred authority on the agent, or authority may be implied. Authority arises by consensual agreement, and whether it exists is a question of fact. An agent, as a general rule, is only entitled to indemnity from the principal if he or she has acted within the scope of her actual authority, and may be in breach of contract, and liable to a third party for breach of the implied warranty of authority. In tort, a claimant may not recover from the principal unless the agent is acting within the scope of employment.
Express actual authority
Express actual authority means an agent has been expressly told he or she may act on behalf of a principal.
Ireland v Livingstone (1872) LR 5 HL 395
Implied actual authority
Implied actual authority, also called "usual authority", is authority an agent has by virtue of being reasonably necessary to carry out his express authority. As such, it can be inferred by virtue of a position held by an agent. For example, partners have authority to bind the other partners in the firm, their liability being joint and several, and in a corporation
, all executives and senior employees with decision-making authority by virtue of their position have authority to bind the corporation.
Hely-Hutchinson v Brayhead Ltd  1 QB 549
 Apparent authority
Main articles: Apparent authority and Estoppel
Apparent authority (also called "ostensible authority") exists where the principal's words or conduct would lead a reasonable person in the third party's position to believe that the agent was authorized to act, even if the principal and the purported agent had never discussed such a relationship. For example, where one person appoints a person to a position which carries with it agency-like powers, those who know of the appointment are entitled to assume that there is apparent authority to do the things ordinarily entrusted to one occupying such a position. If a principal creates the impression that an agent is authorized but there is no actual authority, third parties are protected so long as they have acted reasonably. This is sometimes termed "agency by estoppel" or the "doctrine of holding out", where the principal will be estopped from denying the grant of authority if third parties have changed their positions to their detriment in reliance on the representations made.
Rama Corporation Ltd v Proved Tin and General Investments
Ltd  2 QB 147, Slade J, "Ostensible or apparent authority... is merely a form of estoppel, indeed, it has been termed agency by estoppel and you cannot call in aid an estoppel unless you have three ingredients: (i) a representation, (ii) reliance on the representation, and (iii) an alteration of your position resulting from such reliance."
Freeman & Lockyer v Buckhurst Park Properties (Mangal) Ltd  2 QB 480
The Raffaella or Egyptian International Foreign Trade Co v Soplex Wholesale Supplies Ltd and PS Refson & Co Ltd  2 Lloyd's Rep 36.
BotXXXXX XXXXXne is - you don't owe the alarm company for the equipment.
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