SOLUTION: The owner of Nuts2U Snack Shack mixes cashews worth $6.00 a pound with peanuts worth $2.30 a pound to get a half-pound, mixed-nut bag worth $1.70. How much of each kind of nut i

Algebra ->  Proportions  -> Lessons -> SOLUTION: The owner of Nuts2U Snack Shack mixes cashews worth $6.00 a pound with peanuts worth $2.30 a pound to get a half-pound, mixed-nut bag worth $1.70. How much of each kind of nut i      Log On


   



Question 1056815: The owner of Nuts2U Snack Shack mixes cashews worth $6.00 a pound with peanuts worth $2.30 a pound to get a half-pound, mixed-nut bag worth $1.70.
How much of each kind of nut is included in the mixed bag?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of cashews needed
Let +b+ = pounds of peanuts needed
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(1) +a+%2B+b+=+.5+
(2) +6a+%2B+2.3b+=+1.7+
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(2) +60a+%2B+23b+=+17+
and
(1) +2a+%2B+2b+=+1+
Multiply both sides of (1) by +30+
and subtract (2) from (1)
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(1) +60a+%2B+60b+=+30+
(2) +-60a+-+23b+=+-17+
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+37b+=+13+
+b+=+.351+
and
(1) +a+%2B+b+=+.5+
(1) +a+%2B+.351+=+.5+
(1) +a+=+.149+
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.149 pounds of cashews are needed
.351 pounds of peanuts are needed
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check:
(2) +6a+%2B+2.3b+=+1.7+
(2) +6%2A.149+%2B+2.3%2A.351+=+1.7+
(2) +.894+%2B+.8073+=+1.7+
(2) +1.7013+=+1.7+
error due to rounding off, I think
Definitely get another opinion on this problem