Madelyn has a home-based business making and selling scented soaps. She intially spent $52 to purchase soap-making equipment, and the materials for each kilogram of soap cost $12. Madelyn sells the soap for $25 per kilogram. Eventually, she will sell enough soap to cover the cost of the equipment. What will be Madelyn's total sales and costs be? How much soap will that be?

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?