jackie is 8 years younger than her neighbor Paula. the sum of their ages is 30. how old are jackie and paula?

Let x = Jackie's age

x + x + 8 = 30

2x + 8 = 30

2x = 22

x = 11

Let's break down the information given:

1. Jackie is 8 years younger than Paula.
2. The sum of their ages is 30.

Let's represent Paula's age as "P" and Jackie's age as "J".

Based on the first piece of information, we can write an equation: J = P - 8 (Jackie is 8 years younger than Paula)

Based on the second piece of information, we can write another equation: J + P = 30 (The sum of their ages is 30)

Now we have a system of two equations:

J = P - 8 --------------- (Equation 1)
J + P = 30 -------------- (Equation 2)

We can solve this system of equations using substitution or elimination method. Let's use substitution.

Substitute the value of J from Equation 1 into Equation 2:

(P - 8) + P = 30
2P - 8 = 30
2P = 30 + 8
2P = 38

Divide both sides of the equation by 2:

P = 38 / 2
P = 19

Now substitute the value of P into Equation 1 to find J:

J = 19 - 8
J = 11

Therefore, Paula is 19 years old and Jackie is 11 years old.

To find the ages of Jackie and Paula, we can set up a system of equations based on the information given.

Let's assume Jackie's age is x years.

According to the problem, Paula is 8 years older than Jackie. So, Paula's age would be (x + 8).

The sum of their ages is 30. Therefore, the equation would be:

x + (x + 8) = 30

Simplifying this equation, we get:

2x + 8 = 30

Subtracting 8 from both sides:

2x = 22

Dividing by 2:

x = 11

So Jackie is 11 years old.

To find Paula's age, we substitute this value of x back into the equation:

Paula's age = x + 8 = 11 + 8 = 19

Therefore, Jackie is 11 years old, and Paula is 19 years old.