The number of counties in state A and the number of counties in state B are consecutive even integers whose sum is 114. If state A has more counties than state B, how many counties does each state have?

The number of counties in state A = 56

The number of counties in state B = 58.

Step-by-step explanation:

Let the number of countries in state A = k

So, the number of state in state B = (k+2)

(as he next consecutive even integer after k is k + 2)

Now, according to the question:

k + (k+2) = 114

or, 2k + 2 = 114

⇒ 2k = 114 - 2 = 112

⇒ k = 112/2 = 56

or, k = 56

Hence, the number of counties in state A = k = 56

and the number of counties in state B = k + 2 = 56 + 2 = 58.