SOLUTION: A grocer mixes peanuts that cost $1.49 per pound and walnuts that cost $2.69 per pound to make 100 pounds of a mixture that costs $2.21 per pound. How much of each kind of nut is p
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Question 1158768: A grocer mixes peanuts that cost $1.49 per pound and walnuts that cost $2.69 per pound to make 100 pounds of a mixture that costs $2.21 per pound. How much of each kind of nut is put into the mixture?
Found 3 solutions by josgarithmetic, VFBundy, greenestamps:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
v, the expensive nut $2.69 per pound
100-v, the nut for $1.49 per pound
Solve for v.
.
.
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
Lbs. of peanuts = p
Lbs. of walnuts = w
p + w = 100
1.49p + 2.69w = 2.21(100)
p + w = 100
1.49p + 2.69w = 221
Multiply first equation by -2.69:
-2.69p - 2.69w = -269
1.49p + 2.69w = 221
Add equations together:
-1.20p = -48
p = 40
Since we now know p = 40...and p + w = 100...that means w = 60.
Lbs. of peanuts = p = 40
Lbs. of walnuts = w = 60
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
A quick solution method, without algebra....
(1) Find where 2.21 lies between 1.49 and 2.69:
2.69-1.49 = 1.20
2.21-1.49 = 0.72
0.72/1.20 = 0.6 = 3/5
(2) 2.21 is 3/5 of the way from 1.49 to 2.69; that means 3/5 of the mixture needs to be the more expensive ingredient.
(3) 3/5 of 100 pounds is 60 pounds.
ANSWER: 60 pounds of walnuts; 40 pounds of peanuts
CHECK:
60(2.69)+40(1.49) = 161.40+59.60 = 221
100(2.21) = 221
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