The sum of two consective numbers is divided by their positive difference is equal to 9. Find the larger number
The difference between two consecutive integers is 1, right?
If x is the larger, then x-1 is the smaller. So,
(x-1 + x)/(1) = 9
x = 5
Check: 4+5 = 9
Kinda stupid, setting it up so you divide by 1. Just sayin' ...
x+(x+1) / |x-(x+1)| = 9
2x+1 = 9
x = 4
the two number are 4 and 5.
(x + (x+1))/((x+1)-x) = 9
x+x+1 = 9x+9-9x
2x = 8
X = 4 = smaller number.
x+1 = 5 = larger number.
To solve this problem, we need to translate the given information into an equation and use algebra to find the solution. Let's break it down step by step:
Let's assume that the first consecutive number is x. Therefore, the second consecutive number would be x + 1 because they are consecutive.
The problem states that "the sum of two consecutive numbers is divided by their positive difference is equal to 9." In equation form, this can be represented as:
(x + (x + 1)) / (x - (x + 1)) = 9
Simplifying the equation, we have:
(2x + 1) / (x - x - 1) = 9
(2x + 1) / (-1) = 9
Multiplying both sides by -1 to eliminate the denominator:
2x + 1 = -9
Subtracting 1 from both sides:
2x = -10
Dividing by 2:
x = -5
Since the problem asks for the larger number, which is the second consecutive number, we can find it by adding 1 to x:
x + 1 = -5 + 1 = -4
Therefore, the larger number is -4.