SOLUTION: I need help with this problem, tristian paid $17.50 to buy 2 pounds of peanuts and 3 pounds of cashews. Rivka paid $19.00 to buy 5 pounds of peanuts and 2 pounds of cashews. If bot

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: I need help with this problem, tristian paid $17.50 to buy 2 pounds of peanuts and 3 pounds of cashews. Rivka paid $19.00 to buy 5 pounds of peanuts and 2 pounds of cashews. If bot      Log On


   

Question 1026525: I need help with this problem, tristian paid $17.50 to buy 2 pounds of peanuts and 3 pounds of cashews. Rivka paid $19.00 to buy 5 pounds of peanuts and 2 pounds of cashews. If both paid the same price per pound, what was the price per pound for the cashews?
Found 2 solutions by rothauserc, mananth:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
1) 2p + 3c = 17.50
2) 5p + 2c = 19.00
:
Solve equation 1 for p
:
p = (17.50 - 3c) / 2
:
Substitute for p in second equation
:
(5(17.50 - 3c) / 2) + 2c = 19.00
:
Multiply both sides of = by 2
:
(5(17.50 - 3c)) + 4c = 38.00
:
87.50 - 15c + 4c = 38.00
:
-11c = -49.50
:
c = 4.50
:
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Cashews are $4.50 per pound
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:

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
x= cost of cashew
y= cost of peanuts
Total sold
3.00 x + 2.00 y = 17.50 .............1
Total value
2.00 x + 5.00 y = 19.00 .............2
Eliminate y
multiply (1)by -5.00
Multiply (2) by 2.00
-15.00 x -10.00 y = -87.50
4.00 x + 10.00 y = 38.00
Add the two equations
-11.00 x = -49.50
/ -11.00
x = 4.50
plug value of x in (1)
3.00 x + 2.00 y = 17.50
13.50 + 2.00 y = 17.50
2.00 y = 17.50 -13.50
2.00 y = 4.00
y = 2.00
x= 4.50 cost of cashew
y= 2.00 cost of peanuts
m.ananth@hotmail.ca