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

Answer:

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

Step-by-step 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