(b) That's wrong. B is only 17 years old and this makes her a minor (a person who has not yet reached the age of majority). In Australia, a person legally becomes an adult at the age of 18. Until then, minors have only a limited capacity to bind themselves by contract. This protects young persons from the dangers of entering into contracts that may disadvantage them. But, because it is important for minors to acquire necessities, legislation in the various states and territories make special provision for such cases.
Essentially, if 'necessities' are sold and delivered to a minor (or other person with limited contractual capacity), they must pay a reasonable price for what they have received.
In the example, the household goods are likely to be considered necessities and A would be entitled to recover a reasonable price from B. This may be less than the agreed price if the agreed price is found by the court to be higher than is reasonable for the goods in question. Note: A minor may also be liable to pay a reasonable price for other necessities provided to them, such as accommodation and medical services.