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!