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24 October, 18:06

A food store makes a 11-pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use?

A. 3lbs peanuts, 6 lbs almonds, 2 lbs raisins

B. 8 lbs peanuts, 1 lb almonds, 2 lbs raisins

C. 6 lbs peanuts, 3 lbs almonds, 2 lbs raisins

D. 8 lbs peanuts, 2 lbs almonds, 1 lbs raisins

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Answers (1)
  1. 24 October, 18:57
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    Given: 11-pound mixture of peanuts, almonds, and raisins

    Cost:

    peanuts - 1.5 per pound

    almonds - 3 per pound

    raisins - 1.5 per pound

    mixture:

    twice as many peanuts as almond; total cost of mixture is 21.

    a + p + r = 11 lbs

    a + 2a + r = 11 lbs

    3a + r = 11

    r = 11 - 3a

    1.5 (2a) + 3a + 1.5r = 21

    3a + 3a + 1.5r = 21

    6a + 1.5r = 21

    6a + 1.5 (11-3a) = 21

    6a + 16.5 - 4.5a = 21

    6a - 4.5a = 21 - 16.5

    1.5a = 4.5

    1.5a/1.5 = 4.5/1.5

    a = 3

    almonds = 3 lbs

    peanuts = 2a = 2 (3) = 6lbs

    raisins = 11 - 3a = 11 - 3 (3) = 11 - 9 = 2 lbs

    My answer is: C. 6 lbs peanuts, 3 lbs almonds, 2 lbs raisins
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