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Hi Lucy, I completely agree with RD that the guess and check method is far from the best way to approach this problem. I would use some logic and basic arithmetic. The 10 pound mixture is 50% peanuts so it is 50% not peanuts, that is there are 5 pounds of nonpeanuts in the mixture. When you add more peanuts the number of pounds of nonpeanuts doesn't change. Thus in the final mixture the 5 pounds of nonpeanuts is 40% of the mixture. To get from 40% to 60% you multiply by $\frac64$ and hence 60% of the new mixture is $5 \times \frac64 = 7.5 \mbox{ pounds.}$ Hence you need to add 2.5 pounds of peanuts to the 5 pounds you already have to have the new mixture contain 60% peanuts. Penny  


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