Annie works as both a carpenter and a blacksmith. Last week she worked 12 hours as a carpenter and 20 hours as a blacksmith and earned a total of $860. This week, she worked 6 hours as a carpenter and 26 hours as a blacksmith. Her pay this week was $830. How much does she get paid per hour for each job?

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?