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Kate is 39 years old. Let's break it down. Let's call Kate's age K. Kate's age 13 years ago is K - 13, and her age 13 years from now is K + 13. Her age 13 years ago is half of what it will be in 13 years. The equation that says that is K - 13 = (K + 13) divided by 2. Turn the crank and out pops the answer. K - 13 = (K + 13) divided by 2 [Multiply both sides by 2] 2(K - 13) = K + 13 [Apply the distributive property of multiplication] 2K - 26 = K + 13 [Subtract K from both sides] K - 26 = 13 [Add 26 to both sides] K = 39 Check work. The 39 - 13 = 26, and the 39 + 13 = 52. The 26 is half of 52. We're good.

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