SOLUTION: A nut shop sells almonds for $1.80 a pound, walnuts for $1.30, and peanuts for $.65 a pound. the shopkeeper makes a mixture of 21 pounds of these nuts to sell for $1.00 a pound. he

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: A nut shop sells almonds for $1.80 a pound, walnuts for $1.30, and peanuts for $.65 a pound. the shopkeeper makes a mixture of 21 pounds of these nuts to sell for $1.00 a pound. he      Log On

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Question 697694: A nut shop sells almonds for $1.80 a pound, walnuts for $1.30, and peanuts for $.65 a pound. the shopkeeper makes a mixture of 21 pounds of these nuts to sell for $1.00 a pound. he used twice as many pounds of peanuts as walnuts. how much of each kind of nut did he use?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of almonds needed
Let +b+ = pounds of walnuts needed
Let +c+ = pounds of peanuts needed
given:
(1) +a+%2B+b+%2B+c+=+21+
(2) +%28+1.8a+%2B+1.3b+%2B+.65c+%29+%2F+21+=+1+ ( the +1+ is $1/pound )
(3) +c+=+2b+
-------------
This is 3 equations with 3 unknowns, so it's solvable
(2) +1.8a+%2B+1.3b+%2B+.65c+=+21+
(2) +180a+%2B+130b+%2B+65c+=+2100+
(2) +36a+%2B+26b+%2B+13c+=+420+
----------------------------
Multiply both sides of (1) by +13+
and subtract (1) from (2)
(2) +36a+%2B+26b+%2B+13c+=+420+
(1) +-13a+-+13b+-+13c+=+-273+
+23a+%2B+13b+=+147+
+23a+=+147+-+13b+
+a+=+%28+147+-+13b+%29+%2F+23+
Substitute this result and (3) into (1)
(1) +a+%2B+b+%2B+c+=+21+
(1) +%28+147+-+13b+%29+%2F+23+%2B+b+%2B+2b+=+21+
(1) +147+-+13b+%2B+23b+%2B+46b+=+483+
(1) +56b+=+483+-+147+
(1) +56b+=+336+
(1) +b+=+6+
and, since
(3) +c+=+2b+
(3) +c+=+2%2A6+
(3) +c+=+12+
and
(1) +a+%2B+b+%2B+c+=+21+
(1) +a+%2B+6+%2B+12+=+21+
(1) +a+=+21+-+18+
(1) +a+=+3+
3 pounds of almonds are needed
6 pounds of walnuts are needed
12 pounds of peanuts are needed
check answer:
(2) +%28+1.8a+%2B+1.3b+%2B+.65c+%29+%2F+21+=+1+
(2) +%28+1.8%2A3+%2B+1.3%2A6+%2B+.65%2A12+%29+%2F+21+=+1+
(2) +5.4+%2B+7.8+%2B+7.8+=+21+
(2) +21+=+21+
OK