This is an algebra word problem that can be solved by setting up a system of equations. Stay with me! It only sounds complicated, but we will make it easy.

We have two consecutive integers, let's call them x and y.

Let's say y comes after x, so that means y = x+1 (consecutive numbers are in sequence, like counting, each number is 1 more than the number before it)

Now let's use our other clue from the problem. The larger number is 15 more than twice the smaller.

y is the larger number, and that is 15 more than 2 times the smaller number (x)

y = 15 + 2x

Ok, now let's use substitution.

y = x+1, so we plug that into our equation.

x + 1 = 15 + 2x

Get the variable terms on the left and the constant terms on the right.

x + 1 = 15 + 2x

- 2x -2x

-x + 1 = 15

- 1 -1

-x = 14

*-1 *-1

x = -14

Plug our value of x back into our definition of y.

y = -14 + 1

y = -13

So we have -14 and -13. This makes sense because integers can be negative, -14 and -13 are consecutive, and if we multiply the smaller number (-14) by 2, then add 15, we get -13. Our answer checks out!