A conveniennce store owner wishes to mix raisins and roasted peanuts to make a h

Question

A conveniennce store owner wishes to mix raisins and roasted peanuts to make a high energy snack.  The raisins cost $3.00/kg and the nuts cost $4.50/kg.  How many kilograms of raisins should be included with the peanuts to make 24 kg of the snack costing $4.00/kg?   show each step

Explanation / Answer

r = weight of raisins, measured in kg p = weight of peanuts, measured in kg W = weight of mixture, measured in kg = r + p C = cost of mixture, measured in dollars = 3r + 4.5p CPK = cost of mixture, measured in dollars per kg of mixture = C /W = (3r + 4.5p) / (r + p) Find r and p such that CPK = $4 / kg and W = 24 kg 3r + 4.5p = ? CPK = 4, W = 24 => C / 24 = 4 => (3r + 4.5p) / 24 = 4 =>3r + 4.5p = 24(4) = 96 To find r and p, solve the system of equations: r + p = 24 3r + 4.5p = 96 Multiply each term of [r + p = 24] by -3 to get -3r + -3p = -72 (each term was multiplied by -3) 3r + 4.5p = 96 Add the two equations to get (0)r + 1.5p = 24 => p = 24/1.5 = 16 Use p to find r (remember that r + p = 24) p = 16 => r = 24 - 16 = 8 Final answer: 16 kg of nuts, 8 kg raisins

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