the greater of two consecutive integers is 20 more than twice the smaller. what are the integers
n and n+1
n+1 = 20 + 2n
n = -19
n+1 = -18
To solve this problem, let's assume that the smaller integer is represented by the variable "x."
According to the problem, the larger integer is 20 more than twice the smaller. Therefore, we can represent the larger integer as (2*x) + 20.
Since the two integers are consecutive, the larger integer must be one more than the smaller. So, we can write an equation:
(2*x) + 20 = x + 1
Now, we can solve this equation to find the value of x, which represents the smaller integer.
First, let's simplify the equation:
2*x + 20 = x + 1
Next, let's isolate the variable x on one side of the equation by subtracting x from both sides:
2*x - x + 20 = x - x + 1
Simplifying further:
x + 20 = 1
Now, let's isolate x by subtracting 20 from both sides:
x + 20 - 20 = 1 - 20
Simplifying:
x = -19
Therefore, the smaller integer (x) is -19.
To find the larger integer, substitute this value of x into our expression for the larger integer:
(2*x) + 20 = (2*(-19)) + 20 = -38 + 20 = -18
Therefore, the larger integer is -18.
So, the two consecutive integers that satisfy the given conditions are -19 and -18.