SOLUTION: A coffee distributor needs to mix a(n) Rift Valley coffee blend that normally sells for $8.00 per pound with a Mexican Shade Grown coffee blend that normally sells for $10.40 per p

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Question 1033350: A coffee distributor needs to mix a(n) Rift Valley coffee blend that normally sells for $8.00 per pound with a Mexican Shade Grown coffee blend that normally sells for $10.40 per pound to create 20 pounds of a coffee that can sell for $8.12 per pound. How many pounds of each kind of coffee should they mix?
A) Write an equation using the information as it is given above that can be solved to answer the question. Use x as your variable to represent the quantity of Rift Valley coffee blend.
Equation:
They must mix 
 pounds of the Rift Valley Blend 
pounds of the Mexican Shade Grown Blend. 
Round your answers to the nearest whole number of pounds.
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of Rift Valley coffee
blend needed
Let +b+ = pounds of Mexican Shade Grown
coffee needed
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(1) +a+%2B+b+=+20+
(2) +%28+8a+%2B+10.4b+%29+%2F+20+=+8.12+
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(2) +8a+%2B+10.4b+=+162.4+
(2) +80a+%2B+104b+=+1624+
(2) +10a+%2B+13b+=+203+
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Multiply both sides of (1) by +10+
and subtract (1) from (2)
(2) +10a+%2B+13b+=+203+
(1) +-10a+-+10b+=+-200+
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+3b+=+3+
+b+=+1+
and
(1) +a+%2B+1+=+20+
(1) +a+=+19+
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19 pounds of Rift Valley coffee
blend are needed
1 pound of Mexican Shade Grown
coffee is needed
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check:
(2) +%28+8a+%2B+10.4b+%29+%2F+20+=+8.12+
(2) +%28+8%2A19+%2B+10.4%2A1+%29+%2F+20+=+8.12+
(2) +%28+152+%2B+10.4+%29+%2F+20+=+8.12+
(2) +162.4+=+20%2A8.12+
(2) +162.4+=+162.4+
OK

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A coffee distributor needs to mix a(n) Rift Valley coffee blend that normally sells for $8.00 per pound with a Mexican Shade Grown coffee blend that normally sells for $10.40 per pound to create 20 pounds of a coffee that can sell for $8.12 per pound.
How many pounds of each kind of coffee should they mix?
Quantity Eq:: e + t = 20 lbs
Value Eq:::: 8e + 10.4t = 8.12*20
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8e + 8t = 8*20
8e + 10.4t = 162.4
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Subtract and solve for "t":
2.4t = 2.4
t = 1 lb (amt. of $10.40 coffee needed)
------
e = 20-1 = 19 lb (amt. of $8 coffee needed)
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Cheers,
Stan H.
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