Given positive integers x and y, if the product of the mixed numbers 3 1/x and y 2/5 equals 13 3/4, where the fractions are in simplest form, what are the values of x and y?

Explanation

We have (3 + 1/x) multiplied by (y + 2/5) equal to 13 3/4. Converting mixed numbers to improper fractions, this becomes (3x + 1)/x times (5y + 2)/5 equals 55/4. Testing the options, only when x = 8 and y = 4 does the equation hold true: (25/8) * (22/5) = 55/4, which is 13 3/4.