SOLUTION: A store manager wants to mix two different brands of coffee to make 480 pounds to sell at $2.68 a pound. He uses a brand of coffee worth $2.50 a pound and another brand worth $2.80
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Question 1168287: A store manager wants to mix two different brands of coffee to make 480 pounds to sell at $2.68 a pound. He uses a brand of coffee worth $2.50 a pound and another brand worth $2.80 a pound. How many pounds of each should be used?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
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mix two different brands of coffee to make 480 pounds to sell at $2.68 a pound. He uses a brand of coffee worth $2.50 a pound and another brand worth $2.80 a pound.
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L=2.5
T=2.68
H=2.8
M=480
v, unknown quantity of the H dollars per pound coffee
M-v, amount of the L dollars per pnd. coffee
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Substituting the values given,
-----------you can finish from here.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!
That other tutor really loves that general formula with all those different variables....
I'm more in favor of a student UNDERSTANDING how to solve a problem, rather than plugging numbers into a mysterious formula.
Algebraically, x pounds at $2.50 per pound, plus (480-x) pounds at $2.80 per pound, makes 180 pounds at $2.68 per pound:
Solve using basic algebra; although the calculations are a bit messy.
Here is a quick and easy path to the solution to any 2-part mixture problem like this, if a formal algebraic solution is not required.
Picture the three prices on a number line: 2.50, 2.68, and 2.80.
Determine with simple arithmetic that 2.68 is 18/30 = 3/5 of the way from 2.50 to 2.80.
That means 3/5 of the mixture is the higher priced coffee.
ANSWER: 3/5 of the 480 pounds, or 288 pounds, of the $2.80 coffee; the other 192 pounds of the $2.50 coffee.
CHECK:
288(2.80)+192(2.50) = 806.4+480 = 1286.4
480(2.68) = 1286.4
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