Twice the greater of two consecutive odd integers is 13 less than three times the lesser. Find the integers.
Let x be the greater integer.
2x = 3 (x-2) - 13 = 3x -19
Solve for x (which will indeed be an odd integer) , and subtract 2 for the other odd integer.
Let's represent the two consecutive odd integers as n and n+2.
According to the given condition, twice the greater of two consecutive odd integers is 13 less than three times the lesser. Mathematically, this can be written as:
2(n+2) = 3n - 13
Simplifying the equation, we have:
2n + 4 = 3n - 13
Rearranging the equation:
-13 + 4 = 3n - 2n
-9 = n
Therefore, the first odd integer is -9.
The second odd integer can be found by adding 2 to the first odd integer:
-9 + 2 = -7
So, the two consecutive odd integers are -9 and -7.
Let's assume the first odd integer is x, then the next consecutive odd integer will be x + 2.
According to the given information, twice the greater integer (x + 2) is 13 less than three times the lesser integer (x):
2(x + 2) = 3x - 13
Now, let's solve this equation to find the values of x and x + 2.
2x + 4 = 3x - 13
Subtracting 2x from both sides:
4 = x - 13
Adding 13 to both sides:
x = 17
Therefore, the first odd integer is 17, and the second consecutive odd integer is 17 + 2 = 19.
Hence, the two integers are 17 and 19.