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!
10/23/2013

Katherine P.