Answer:
Smaller integer = 195
Larger integer = 196
Explanation:
We can find the two integers using a system of equations, where
- x represents the smaller integer,
- and y represents the larger integer.
First equation:
Since the sum of the two integers is 391, our first equation is given by:
x + y = 391
Second equation:
We know that for any two consecutive integers, the difference is always 1 when the smaller integer is subtracted from the larger (e.g., 2 - 1 = 1, 100 - 99 = 1, etc.).
Thus, our second equation:
y - x = 1
For ease when solving, we can write it as:
-x + y = 1
Method to solve: Elimination:
Solving for y:
The two equations are arranged in a way that will allow us to solve for y and eliminate the xs when adding since x - x = 0:
x + y = 391
+
-x + y = 1
----------------------------------------------------------------------------------------------------------(x - x) + (y + y) = (391 + 1)
(2y = 392) / 2
y = 196
Thus, y = 196.
Solving for x:
Now we can solve for x by plugging in 196 for y in the first equation:
(x + 196 = 391) - 196
x = 195
Thus, x = 195.