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sue plans to mix pepper mints worth $1.20 per lb with chocolates worth $2.40 per lb to get a 40 lb mix that is worth $1.65 per lb. How much of each should she use?
Let 'x' be the amount of pepper mints ($1.20 per pound) 'y' be the amount of chocolates ($2.40 per pound) ------------------------- -The whole mixture amounts to 40 lbs. x + y = 40 ----------equation 1 ------------------------ -The mix is $1.65 per pound 1.2x + 2.4y = 40(1.65) 1.2x + 2.4y = 66 ----equation 2 ----------------------- From equation 1 x + y = 40 x = 40 - y ----equation 3 --------------------- Substitute equation 3 to equation 2 1.2x + 2.4y = 66 1.2(40-y) + 2.4y = 66 48 - 1.2y + 2.4y = 66 -1.2y + 2.4y = 66 - 48 1.2y = 18 y = 15 lbs -------------------- Substitute y=15 to equation 3 x = 40 - y x = 40 - 15 x = 25 lbs -------------------- Therefore 15 lbs of chocolates and 25 lbs of pepper mints will be used.
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