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 Question from Andrew, a student: How many kg of mixed nuts that contain 30% peanuts must Paul add to 6kg of mixed nuts that contain 38% peanuts to make a mixture that contains 33% peanuts?

Hi Andrew,

Let the weight of the final mixture be $x$ km and then the final mixture contains $0.33 \times x$ kg of peanuts. The weight of the peanuts in the original $6$ kg is $0.38 \times 6 = 2.28 \mbox{ kg.}$ Since the weight of the final mixture is $x$ kg he must add $x - 6$ kg of the $30 \%$ mixture. The weight of the peanuts in what he adds is $0.30 \times (x - 6)$ kg. The weight of peanuts in the original mixture plus the weight of peanuts he adds must be the weight of peanuts in the final mixture. Solve for $x.$

Penny

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