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) About Me  (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

Hv%2BL%28M-v%29=MT
-
Hv-Lv%2BML=MT
%28H-L%29v=MT-ML
highlight%28v=M%28%28T-L%29%2F%28H-L%29%29%29

Substituting the values given,
v=480%28%280.68-0.5%29%2F%280.8-0.5%29%29
v=480%2A%280.18%2F0.3%29
v=480%2818%2F30%29=highlight_green%28480%283%2F5%29%29-----------you can finish from here.

Answer by greenestamps(13203) About Me  (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:

x%282.50%29%2B%28480-x%29%282.80%29+=+480%282.68%29

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