find the positive difference between to consecutive even integers such that 14 times the first is equal to 12 times the second
Huh? The difference between any two consecutive even integers is 2!
14(2k) = 12(2k+2)
28k = 24k+24
4k = 24
k = 6
the numbers are 12 and 14, so the difference is 2
To find the positive difference between two consecutive even integers, we need to set up an equation based on the given information.
Let's assume the first even integer as 'x'. Since it is an even integer, the next consecutive even integer will be 'x + 2'.
According to the given information, 14 times the first even integer is equal to 12 times the second even integer:
14x = 12(x + 2)
Now, let's solve this equation to find the value of 'x':
14x = 12x + 24 (by distributing 12 to x and 12 to 2)
2x = 24 (subtracting 12x from both sides)
x = 12 (dividing by 2)
So, the first even integer is 12, and the second even integer is 12 + 2 = 14.
Now, let's find the positive difference between the two consecutive even integers:
Positive difference = second integer - first integer
= 14 - 12
= 2
Therefore, the positive difference between the two consecutive even integers is 2.