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

Algebra ->  Algebra  -> Expressions-with-variables -> SOLUTION: Nine pounds of sweep potatoes cost the same as 6 pounds of apples. One pound of sweet potatoes cost twice as much as a pound of onions, while a pound of apples cost 24 ents more th      Log On

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Question 173441: Nine pounds of sweep potatoes cost the same as 6 pounds of apples. One pound of sweet potatoes cost twice as much as a pound of onions, while a pound of apples cost 24 ents more than a pound of onions. Fidn the cost of each.
Answer by solver91311(16872) About Me  (Show Source):
You can put this solution on YOUR website!
Let the cost of one lb. of sweet potatoes = s
Let the cost of one lb. of apples = a
Let the cost of one lb. of onions = n (I chose n to represent onions so that there is no possibility that o ("oh") can be confused with 0 ("zero").

Givens:
1. 9s=6a
2. s=2n
3. a=n%2B24

Use substitution:
cartoon%289%2Ared%28s%29=6%2Agreen%28a%29%2C9%2Ared%282n%29=6%2A%28green%28n%2B24%29%29%29

18n=6n%2B144

12n=144

n=12

Since the only given constant value was expressed in cents, the value of n must also be in cents. Hence, onions cost 12 cents per pound.

Apples, then, must cost 12%2B24=36 cents per pound and sweet potatoes cost 2%2812%29=24 cents per pound.

Either this is a VERY old problem, or I want to know where to find this grocery store!