SOLUTION: Sarah Meehan blends coffee for taste-delight. She needs to prepare 160 pounds of coffee beans selling for $5.19 per pound. She plans to do this by blending together a high-quality

Question 1047143: Sarah Meehan blends coffee for taste-delight. She needs to prepare 160 pounds of coffee beans selling for $5.19 per pound. She plans to do this by blending together a high-quality bean costing $6.50 per pound and a cheaper bean at $3.50 per pound. To the nearest pound find how much high quality coffee bean and how much cheaper coffee bean she should blend.
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Sarah Meehan blends coffee for taste-delight. She needs to prepare 160 pounds of coffee beans selling for $5.19 per pound. She plans to do this by blending together a high-quality bean costing $6.50 per pound and a cheaper bean at $3.50 per pound. To the nearest pound find how much high quality coffee bean and how much cheaper coffee bean she should blend.
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Using 2 variables::
H + L = 160 lbs
6.5H + 3.5L = 5.19*160
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65H + 65L = 65*160
65H + 35L = 51.9*160
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Substract and solve for "L"::
30L = 13.1*160
L = 69.87 lbs (amt. of lower priced coffee)
H = 160-69.87 = 90.13 lbs (amt. of higher priced coffee)
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Cheers,
Stan H.
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Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = pounds of high-quality beans needed
Let = pounds of cheaper beans needed
-------------------------------------------
(1)
(2)
----------------------------------
(2)
(2)
(2)
Multiply both sides of (1) by and
subtract (1) from (2)
(2)
(1)
---------------------------

and
(1)
(1)
(1)
----------------------------
She needs:
90 pounds of the high quality beans
70 pounds of the cheaper beans
-----------------------------------
check:
(2)
(2)
(2)
(2)
(2)
close enough

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