SOLUTION: Nine pounds of sweet potatoes cost the same as 6 pounds of apples. One pound of sweet potatoes costs twice as much as a pound of onions, while a pound of apples costs 24 cents more

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Question 119485: Nine pounds of sweet potatoes cost the same as 6 pounds of apples. One pound of sweet potatoes costs twice as much as a pound of onions, while a pound of apples costs 24 cents more than a pound of onions. Find the cost of each.
Answer by MaxLiebling(13) About Me  (Show Source):
You can put this solution on YOUR website!
Nine pounds of sweet potatoes (p) cost the same as 6 pounds of apples (a):
9*p = 6*a -> 3p = 2a (1)
One pound of sweet potatoes costs twice as much as a pound of onions (n):
1*p = 2 * 1*n -> p = 2n -> 3p = 6n (2)
a pound of apples costs 24 cents more than a pound of onions:
1*a = 1*n + 24 cent -> a = n + 24 cent (3)
----
(1) 3p = 2a
(2) 3p = 6n
-----------
-> 2a = 6n
-> a = 3n
(3) a = n + 24 cent
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-> 3n = n + 24 cent
-> 2n = 24 cent
-> n = 12 cent
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(3) a = n + 24 cent = 12 cent + 24 cemt = 36 cent
a = 36 cent
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(1) 3p = 2a = 2 * 36 cent = 72 cent
-> p = 24 cent
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proof:
9*p = 6*a
9*p = 9*24cent = 218 cent
6*a = 6*36cent = 218 cent ok.
1*p = 2 * 1*n
1*p = 24cent
2*n = 2*12cent = 24cent ok.
1*a = 1*n + 24 cent
1*a = 36cent
n + 24cent = 12cent + 24cent = 36cent ok.