SOLUTION: Four pounds of onions cost the same as 2 pounds of string beans. At the same time, 1 pound of string beans costs 3 times as much as a pound of potatoes, while one pound of onions c

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Four pounds of onions cost the same as 2 pounds of string beans. At the same time, 1 pound of string beans costs 3 times as much as a pound of potatoes, while one pound of onions c      Log On


   



Question 1157877: Four pounds of onions cost the same as 2 pounds of string beans. At the same time, 1 pound of string beans costs 3 times as much as a pound of potatoes, while one pound of onions costs 4 cents less than 2 pounds of potatoes. What is the total cost (without tax) of 1 pound of each of the vegetables?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the cost per pound of onions
Let +b+ = the cost per pound of string beans
Let +c+ = the cost per pound of potatoes
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(1) +4a+=+2b+
(2) +b+=+3c+
(3) +a+=+2c+-+.04+
----------------------------
(3) +2c+=+a+%2B+.04+
(3) +c+=+.5a+%2B+.02+
Plug this into (2)
(2) +b+=+3%2A%28+.5a+%2B+.02+%29+
(2) +2b+=+6%2A%28+.5a+%2B+.02+%29+
(2) +2b+=+3a+%2B+.12+
Plug this resuilt into (1)
(1) +4a+=+3a+%2B+.12+
(1) +a+=+.12+
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(1) +4%2A.12+=+2b+
(1) +2b+=+.48+
(1) +b+=+.24+
----------------------
(3) +a+=+2c+-+.04+
(3) +.12+=+2c+-+.04+
(3) +2c+=+.16+
(3) +c+=+.08+
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$0.12 = the cost per pound of onions
$0.24 = the cost per pound of string beans
$0.08 = the cost per pound of potatoes
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check:
(1) +4a+=+2b+
(1) +4%2A.12+=+2%2A.24+
(1) +.48+=+.48+
and
(2) +b+=+3c+
(2) +.24+=+3%2A.08+
(2) +.24+=+.24+
and
(3) +a+=+2c+-+.04+
(3) +.12+=+2%2A.08+-+.04+
(3) +.12+=+.16+-+.04+
(3) +.12+=+.12+
OK
check my math!