an integer is one more than four times another. if the product of the two integers is 39, then find the integers

Let's say the integers are x and y. x = 1 + 4y, as the problem says. The problem also says that x * y = 39.

We can substitute 1 + 4y for x and get:

(1 + 4y) * y = 39

Distribute:

y + 4y^2 = 39

Subtract 39 from both sides:

4y^2 + y - 39 = 0

Factor:

(4y + 13) * (y - 3) = 0

Solve for y:

y can equal - 13/4 or 3

The problem says that y must be an integer, so we cross off - 13/4, giving us y = 3.

Use y to solve for x:

x = 1 + 4 * (3) = 13

So, y = 3 and x = 13.