Jayce bought 2 bath towels and returned 3 hand towels. his sister bought 3 bath towels and 3 hand towels. jayce's bill was $5. his sisters was $45. what are the prices of the bath towel and hand towels?

Question and answers are in the attached picture. you so much in advance.

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

It takes an ant farm 3 days to consume 1/2 of an apple. at that rate, in how many days will the ant farm consume 3 apples