SOLUTION: Word problem into a rational equation, 18 lbs of fruit purchased, there where $9 worth of apples and $2.40 of bananas, price per lb of apples is three times more than price per lb

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Question 974226: Word problem into a rational equation, 18 lbs of fruit purchased, there where $9 worth of apples and $2.40 of bananas, price per lb of apples is three times more than price per lb of bananas. How many lbs of apples and how many lbs of bananas where purchased? How do I solve?
My email is cyclo29@yahoo.com thank you!
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Word problem into a rational equation, 18 lbs of fruit purchased, there where $9
worth of apples and $2.40 of bananas, price per lb of apples is three times more
than price per lb of bananas. How many lbs of apples and how many lbs of bananas
where purchased? How do I solve?
My email is cyclo29@yahoo.com thank you!
Let the number of pounds of apples = x.

>>18 lbs of fruit purchased<<
So the number of pounds of bananas = 18-x

price per lb of apples is three times more than price per lb of bananas.
Let the price per pound of bananas = y
Then the price per pound of apples = 3y.

>>...there where $9 worth of apples...<<
%28matrix%286%2C1%2C%0D%0AThe%2Cnumber%2Cof%2Cpounds%2Cof%2Capples%29%29%22%D7%22%28matrix%286%2C1%2C%0D%0AThe%2Cprice%2Cper%2Cpound%2Cof%2Capples%29%29%22%22=%22%22%22%249%22

Therefore:

(x)(3y) = 9
    3xy = 9
     xy = 3

>>...and $2.40 of bananas,...<<
%28matrix%286%2C1%2C%0D%0AThe%2Cnumber%2Cof%2Cpounds%2Cof%2Cbananas%29%29%22%D7%22%28matrix%286%2C1%2C%0D%0AThe%2Cprice%2Cper%2Cpound%2Cof%2Cbananas%29%29%22%22=%22%22%22%242.40%22

Therefore:

(18-x)(y) = 2.40
  y(18-x) = 2.40
   18y-xy = 2.40

So we have the two equations:

system%28xy+=+3%2C18y-xy=2.40%29

Substitute 3 for xy in the second equation:

 18y-xy = 2.40
  18y-3 = 2.40
    18y = 5.40
      y = 0.30, 

[so bananas sold for 30 cents a pound, and apples 90 cents a pound.]

Substitute y = 0.30 in the first equation:

     xy = 3
x(0.30) = 3
      x = 3%2F0.30
      x = 10

So there were 10 pounds of apples purchased.
And therefore there were 18-x or 18-10 or 8 pounds of bananas.

Edwin