A grocery store makes an 11-pound mix of peanuts, almonds and raisins. Peanuts are $1.50 a pound, almonds $3.00 a pound, and raisins $1.50 a pound. The mixture requires twice as many peanuts as almonds. The total mixing cost is $21.00. How much of each ingredient did the store use?
single-variable solution
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x pounds of almonds, then 2x pounds of peanuts and (11-3x) pounds of raisins
3x + 1.5*2x + 1.5(11-3x) = 21
1.5x=21-1.5*11=4.5, x=3
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almonds: 3 pounds
peanut: 6 pounds
raisins: 2 pounds
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guess the volume of peanuts :a
almonds: b
raisins: c
you will have systems of equations below:
a+b+c=11;1.5a+3b+1.5c=21.00;a-2b=0
solving these equations, we will have_a=6;b=3;c=2
peanut: 6 pounds
almonds: 3 pounds
raisins: 2 pounds
Dice: 11 pound mix of peanuts, almonds and raisins
Cost:
peanuts – 1.5 per pound
almonds – 3 per pound
raisins – 1.5 per pound
mixed:
twice as many peanuts as almonds; the total cost of the mixture is 21.
a + p + r = 11 pounds
a + 2a + r = 11 pounds
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
6y + 16.5 – 4.5y = 21
6y – 4.5y = 21 – 16.5
1.5y = 4.5
1.5a/1.5 = 4.5/1.5
one = 3
almonds = 3 pounds
peanut = 2a = 2(3) = 6 pounds
raisins = 11 – 3a = 11 – 3(3) = 11 – 9 = 2 pounds
My answer is: C. 6 pounds peanuts, 3 pounds almonds, 2 pounds raisins
6.5 pounds of peanuts => $9.75
3.25 pounds of almonds => $9.75
1 kilo of raisins => $1.50