Sharla is 8 year older than her sister, patricia. The sum of their ages is 102. Find their ages.

Patricia is 47 years old

Sharla is 55 years old

Step-by-step explanation:

Rewrite the first sentence as an equation: (S = Sharla) (P = Patricia)

S=P+8

Rewrite the second sentence as an equation:

S+P=102

1) Substitute P+8 as Sharla in the second equation:

P+8+P=102

2) Combine alike terms:

2P+8=102

3) Subtract 8 from both sides:

2P=94

4) Divide both sides by 2:

P=47

5) Substitute 47 as P in the First equation:

S=47+8

6) Solve:

S=55

Sharla's age: 55

Patricia's age: 47

Step-by-step explanation:

Let p represent patricia age.

p + (p+8) = 102

If we combine like terms, it will end up like this:

2p+8=102

We have to subtract 8 from both sides.

2p=94

We have to divide 2 from both sides.

p=47

Since Patrica's age is 47, and we already know that Sharla is 8 years older than Patrica, Sharla's age is 47+8, which is 55.

Now, we can check our work. Does 47+55=100? Yes.