SOLUTION: You want to fill nine 1-lb tins with a holiday snack mix. You want the mix to contain the three following items: dried apple pieces which cost $2.45 per pound., pecans which cost $

Question 408325: You want to fill nine 1-lb tins with a holiday snack mix. You want the mix to contain the three following items: dried apple pieces which cost $2.45 per pound., pecans which cost $1.85 per pound, and dried cherry pieces which cost $0.80 per pound. You must spend $15 and want the mix to contain half as many pounds of cherry pieces as dried apple slices and pecans combined. How many pounds of pecans should you buy?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
You want to fill nine 1-lb tins with a holiday snack mix.
You want the mix to contain the three following items:
dried apple pieces which cost $2.45 per pound.,
pecans which cost $1.85 per pound,
and dried cherry pieces which cost $0.80 per pound.
You must spend $15 and want the mix to contain half as many pounds of cherry
pieces as dried apple slices and pecans combined.
How many pounds of pecans should you buy?
:
Let p = lbs of pecans required
Let a = lbs of apples
Let c = lbs of cherrys
:
a + p + c = 9
:
2.45a + 1.85p + .80c = 15
:
"the mix to contain half as many pounds of cherry pieces as dried apple slices and pecans combined.
.5c = a + p
Rearrange as
a + p -.5c = 0
Subtract from the 1st equation
a + p + c = 9
a + p -.5c = 0
-----------------subtracting eliminates a & p, find c
1.5c = 9
c =
c = 6 lb of cherries
then
a + p = .5(6)
a + p = 3
a = (3-p)
:
In the cost equation: replace a with (3-p), replace c with 6, find p
2.45(3-p) + 1.85p + .80(6) = 15
7.35 - 2.45p + 1.85p + 4.80 = 15
-2.45p + 1.85p + 12.15 = 15
-.60p = 15 - 12.15
-.6p = 2.85
p =
p = -4.75, a negative means this problem has a major flaw in it. Can't be done with these values|

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