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Final answer:It will take 25 months for the cost of Plan B with the purchased phone to be equal to the cost of Plan A.Explanation:To determine how many months it will take for the cost of Plan B to be equal to the cost of Plan A, we need to find the total cost of each plan with the additional cost of purchasing the phone for Plan B. Plan A costs $70 per month and includes a free phone, so the total cost per month is $70. Plan B costs $50 per month and the phone costs $500, so the total cost per month is $50 + ($500 / X), where X is the number of months. We can set up an equation to find X:$70 = $50 + ($500 / X)Simplifying the equation:$20 = $500 / XMultiplying both sides of the equation by X:20X = $500Dividing both sides of the equation by 20:X = $500 / 20 = 25Therefore, it will take 25 months for the cost of Plan B with the purchased phone to be equal to the cost of Plan A....

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