A local grocer wants to mix candied pecans, priced at $14.00 /pound (lb), and candied cashews, priced at $10.00//lb. How many pounds of candied cashews must he mix with 8lbs of candied pecans to make a mixture that costs $12.50//lb ? (Round the answer to the nearest tenth of a pound.)

Question

A local grocer wants to mix candied pecans, priced at  $14.00 /pound (lb), and candied cashews, priced at  $10.00//lb. How many pounds of candied cashews must he mix with  8lbs of candied pecans to make a mixture that costs  $12.50//lb ? (Round the answer to the nearest tenth of a pound.)

Bytelearn · Accepted Answer

Denoting the number of pounds: Let's denote the number of pounds of candied cashews needed as x. The total cost of the candied pecans is 8 lbs * $14.00/lb. The total cost of the candied cashews will be x lbs * $10.00/lb. The combined weight of the mixture will be 8 lbs + x lbs, and the total cost of the mixture should be (8 lbs + x lbs) * $12.50/lb. We can set up the equation to represent the total cost of the mixture from both types of nuts.Setting up the equation: The equation based on the total cost of the mixture is: (8 lbs * $14.00/lb) + (x lbs * $10.00/lb) = (8 lbs + x lbs) * $12.50/lbSimplifying and solving for x: Now we simplify and solve for x: $112.00 + $10.00x = $12.50 * (8 lbs + x lbs) $112.00 + $10.00x = $100.00 + $12.50xMoving terms and constants: Next, we'll move all terms involving x to one side and constant terms to the other side: $12.50x - $10.00x = $112.00 - $100.00 $2.50x = $12.00Dividing both sides to solve for x: Now we divide both sides by $2.50 to solve for x: x = $12.00 / $2.50 x = 4.8Rounding the answer: We round the answer to the nearest tenth of a pound as requested: x ≈ 4.8 lbs

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