Question

The number of counties in state A and the number of counties in state B are consecutive even integers whose sum is 162. If state A has more counties than state B, how many counties does each state have?

Answer 1

The number of counties in state A is 82 and the number of counties in state B is 80

Explanation:

Let

x -----> the number of counties in state B

x+2 -----> the number of counties in state A

we know that

The sum of counties in state A and state B must be equal to 162

`x+(x+2)=162`

Solve for x

Group terms that contain the same variable and move the constant to the other side

`x+x=162-2`

Combine like terms

`2x=160`

Divide by 2 both sides

`x=80`

so

`x+2=82`

therefore

The number of counties in state A is 82 and the number of counties in state B is 80