Answer:
Annie is 14 and Anna is 16.
Step-by-step explanation:
The first sentence of the problem states that the sum of their ages is 30. We can treat this as a number problem by saying the sum of two numbers is 30.
If we let x to be Annie's age, then Anna's age is 30 - x.
Then, the next sentence states that Anna's age is 9 years more than half of Annie's age. By translating into a number problem, this is the same as saying 30 - x is equal to 9 plus half of x.
Then, we solve for x.
We then arrive at x = 14. Since Annie's age is x, this means that Annie is 14 years old.
Next, since Anna's age is represented by 30 - x, we substitute 14 for x and we find out that Anna is 16 years old.
We can check this: the sum of their ages, 14 + 16, is indeed 30. Then, provided by Annie's age 14, Anna's age is nine years plus half of 14. Half of 14 is 7, and when 9 is added to 7, we get 16.
We further conclude that Annie is 14 years old and Anna is 16 years old
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