Question

the number of counties in state a and the number of counties in state b are consecutive even integers whose sum is 90. if state a has more counties than state b, how many counties does each state have? state a has counties. state b has counties.

Explanation:

Step1: Let the number of counties in state B be $x$.

Since the numbers are consecutive even - integers and state A has more counties than state B, the number of counties in state A is $x + 2$.

Step2: Set up the sum equation.

The sum of the number of counties in state A and state B is 90. So, $(x)+(x + 2)=90$.

Step3: Simplify the equation.

Combining like - terms, we get $2x+2 = 90$. Subtract 2 from both sides: $2x=90 - 2=88$.

Step4: Solve for $x$.

Divide both sides of the equation $2x = 88$ by 2. So, $x=\frac{88}{2}=44$.

Step5: Find the number of counties in state A.

Since state A has $x + 2$ counties and $x = 44$, then state A has $44+2 = 46$ counties.

Answer:

State A has 46 counties. State B has 44 counties.