The lesser of two consecutive even integers is 10 more than one-half the greater. Find the integers.
22 and 24
To find the integers, let's represent the consecutive even integers as x and x+2, where x is the smaller integer.
According to the problem, the lesser of the two consecutive even integers (x) is 10 more than one-half the greater (x+2). Therefore, we can set up the equation:
x = (1/2)(x+2) + 10
To solve this equation, we'll start by distributing the 1/2 to (x+2):
x = (1/2)x + 1 + 10
Next, we'll combine like terms:
x - (1/2)x = 11
To simplify the equation, we'll multiply all terms by 2 to get rid of the fraction:
2x - x = 22
x = 22
So, the smaller integer is x = 22. Using this value, we can find the other integer:
x+2 = 22 + 2 = 24
Therefore, the two consecutive even integers are 22 and 24.