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.)

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Define Variables: Let x be the number of pounds of candied cashews that need to be mixed with the candied pecans. The price per pound of the mixture is desired to be $12.50.Calculate Pecans Cost: The total cost of the candied pecans is 8 lbs times $14.00 per lb, which is $112.00. Calculation: 8 lbs * $14.00/lb = $112.00Calculate Cashews Cost: The total cost of the candied cashews will be x lbs times $10.00 per lb, which is $10.00x. Calculation: x lbs * $10.00/lb = $10.00xCalculate Total Weight: The total weight of the mixture will be 8 lbs + x lbs. Calculation: 8 lbs + x lbsCalculate Total Cost: The total cost of the mixture will be the sum of the cost of the pecans and the cost of the cashews, which is $112.00 + $10.00x. Calculation: $112.00 + $10.00xSet Price Per Pound Equation: The price per pound of the mixture is found by dividing the total cost by the total weight. We set this equal to the desired price per pound, $12.50. Equation: ($112.00 + $10.00x) / (8 lbs + x lbs) = $12.50/lbClear Fraction: Multiply both sides of the equation by (8 + x) to clear the fraction. Calculation: ($112.00 + $10.00x) = $12.50 * (8 lbs + x lbs)Distribute Price: Distribute $12.50 on the right side of the equation. Calculation: $112.00 + $10.00x = $12.50 * 8 + $12.50xSimplify Equation: Simplify the right side of the equation. Calculation: $112.00 + $10.00x = $100.00 + $12.50xIsolate x Term: Subtract $10.00x from both sides to get all x terms on one side. Calculation: $112.00 = $100.00 + $2.50xSubtract Constant: Subtract $100.00 from both sides to isolate the x term. Calculation: $12.00 = $2.50xSolve for x: Divide both sides by $2.50 to solve for x. Calculation: x = $12.00 / $2.50Final Calculation: Perform the division to find the value of x. Calculation: x = 4.8

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

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