Question 880249: Julie, Frank and Lisa went to the grocery store to purchase some fruit. Julie
bought 2 pounds of apples and 3 pounds of bananas for $4.50. Frank bought 1
pound of apples and 2 pounds of oranges for $4.40. Lisa bought 2 pounds of
bananas and 1 pound of oranges for $3.00. What are the prices per pound for
apples, bananas and oranges?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Julie, Frank and Lisa went to the grocery store to purchase some fruit.
Julie bought 2 pounds of apples and 3 pounds of bananas for $4.50.
Frank bought 1 pound of apples and 2 pounds of oranges for $4.40.
Lisa bought 2 pounds of bananas and 1 pound of oranges for $3.00.
What are the prices per pound for apples, bananas and oranges?
:
let a = price of apples
let b = price of bananas
let c = price of oranges
:
Write an equation for each person
2a + 3b + 0c = 4.50; Julie
1a + 0b + 2c = 4.40; Frank
0a + 2b + 1c = 3.00; Lisa
:
Take the last equation
2b + 1c = 3
c = (3-2b)
replace c in the 2nd equation
a + 2(3-2b) = 4.4
a + 6 - 4b = 4.4
a - 4b = 4.4 - 6
a - 4b = -1.6
Multiply by -2, add to the first equation
-2a + 8b = 3.2
2a + 3b = 4.5
-----------------Addition eliminates a, find b
0 + 11b = 7.7
b = 7.7/11
b = $.70 a lb for bananas
Find c
c = 3 - 2(.7)
c = 3 - 1.40
c = $1.60 a lb for oranges
Find a
2a + 3b = 4.5
replace with .70
2a + 3(.70) = 4.5
2a = 4.5 - 2.1
2a = 2.4
a = 2.4/2
a = $1.20 a lb for apples
:
:
See if this checks out in the 3rd equation
2b + 1c = 3.00
2(.70) + 1.60 = 3
1.40 + 1.60 = 3
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