SOLUTION: a coffee merchant has coffee beans that sell for $9 per pund and &12 per pound. The two types are to be mixed to create 100LB of mixture that will sell for $11.25 per pound. How mu

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Question 87971: a coffee merchant has coffee beans that sell for $9 per pund and &12 per pound. The two types are to be mixed to create 100LB of mixture that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture?
Found 2 solutions by stanbon, tutorcecilia:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
a coffee merchant has coffee beans that sell for $9 per pund and &12 per pound. The two types are to be mixed to create 100LB of mixture that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture?
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Let amt. of $9 beans be "x" lbs; Value of this is 9x dollars
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Amt of $12 beans is "100-x" lbs; Value of this is 12(100-x)=1200-12x dollars
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Amt of mixture = 100 lbs ; value of this is 11.25*100 = 1125 dollars
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EQUATION:
value + value = value of mixture
9x + 1200-12x = 1125
-3x = -75
x = 25 lbs (Amt of $9 beans in the mixture)
100-x = 75 lbs (Amt of $12 beans in the mixture)
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cheers,
Stan H.

Answer by tutorcecilia(2152) (Show Source):
You can put this solution on YOUR website!
Let x = beans @ $9
Let y = beans @ $12
Total cost = (100)(11.25) = $1,125
.
So, x+y= 100lbs
y=100-x
.
$9(x)+$12(y)=$1,125
9x+12(100-x)=1125 [substitute (y=100-x)]
9x+1200-12x=1125 [simplify and combine like-terms]
-3x+1200=1125 [solve for the x-term]
-3x+1200-1200=1125-1200
-3x=-75
-3x/-3x=-75/3
x=25 lbs at $9.00/lb
.
So, plugging in (x=25), solve for the y-term:
x+y=100
25+y=100
y=100-25
y=75 at $12.00/lb
.
Plug-in the x and y values:
$9(x)+$12(y)=$1,125
9(25)+12(75)=1,125
1125=1125 [checks out]