Christine's coffee shop makes a blend that is a mixture of two types of coffee. type a coffee costs christine $5.65 per pound, and type b coffee costs $4.10 per pound. this month, christine made 136 pounds of the blend, for a total cost of $644.40 . how many pounds of type a coffee did she use?

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- 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. 3- 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 part b?