Two thirds of Helen's age is half of Dales age. Dale is 10 years older than Helen. How old is Helen?

Helen is 30. Dale is 40.

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To determine Helen's age, we can solve this problem step by step:

Let's assume Helen's age is H and Dale's age is D.

We know that Dale is 10 years older than Helen, which can be represented as:

D = H + 10

It's also given that two-thirds of Helen's age is half of Dale's age. Translating it into an equation, we have:

(2/3)H = (1/2)D

Since D = H + 10, we can substitute this value into the equation:

(2/3)H = (1/2)(H + 10)

To simplify the equation, we can first multiply each side by 6 to eliminate the fractions:

6 * (2/3)H = 6 * (1/2)(H + 10)

4H = 3(H + 10)

Next, distribute the 3 to (H + 10):

4H = 3H + 30

Subtract 3H from both sides:

H = 30

Therefore, Helen is 30 years old.