# The sum of the ages of two sisters is 12 years, and the difference in their ages is 6 years. What are their ages?

They are 9 and 3.

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Let's denote the age of the older sister as ( O ) and the age of the younger sister as ( Y ).

We know that the sum of their ages is 12:

( O + Y = 12 ) (1)

We also know that the difference in their ages is 6:

( O - Y = 6 ) (2)

Now, we can solve this system of equations. Let's add equation (1) and equation (2) to eliminate ( Y ):

( (O + Y) + (O - Y) = 12 + 6 )

( 2O = 18 )

Divide both sides by 2:

( O = \frac{18}{2} )

( O = 9 )

Now that we know the age of the older sister is 9, we can substitute this value into equation (1) to find the age of the younger sister:

( 9 + Y = 12 )

Subtract 9 from both sides:

( Y = 12 - 9 )

( Y = 3 )

Therefore, the older sister is 9 years old, and the younger sister is 3 years old.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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