SOLUTION: A coffee merchant combines coffee that costs $7 per pound with coffee that costs $3.30 per pound. How many pounds of each should be used to make 25 lb of a blend costing $5.89 per
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Question 1164359: A coffee merchant combines coffee that costs $7 per pound with coffee that costs $3.30 per pound. How many pounds of each should be used to make 25 lb of a blend costing $5.89 per pound?
You can put this solution on YOUR website! A coffee merchant combines coffee that costs $7 per pound with coffee that costs $3.30 per pound.
How many pounds of each should be used to make 25 lb of a blend costing $5.89 per pound?
:
let a = amt of $7 coffee required
the final amt is to be 25 lb, therefore
(25-a) = amt of $3.30 coffee required
:
A typical mixture equation
7a + 3.30(25-a) = 5.89(25)
7a + 82.5 - 3.3a = 147.25
7a - 3.3a = 147.25 - 82.50
3.7a = 64.75
a = 64.75/
a = 17.5 lb of $7 coffee
and
25 - 17.5 = 7.5 lb of $3.30 coffee
:
:
Check this out
7(17.5) + 3.3(7.5) = 5.89(25)
122.50 + 24.75 = 147.25
Another tutor has shown a solution by the standard algebraic method. It is a method you should know and be able to use, as it is applicable to a wide range of similar two-part "mixture" problems.
If speed of finding an answer is important (as in a timed math competition) and formal algebra is not required, here is a quick way to answer any question like this with logical reasoning and some mental arithmetic.
(The mental arithmetic in this example might be a stretch for many students; but the path to the final answer will still be faster than with formal algebra.)
Consider the three per-pound prices on a number line: 3.30, 5.89, and 7.00.
The price of the mixture is 259/370 = 7/10 of the way from 3.30 to 7.00. (3.30 to 7.00 is a difference of 3.70; 3.30 to 5.89 is a difference of 2.59. 2.59/3.70 = 259/370 = 7/10.)
That means 7/10 of the mixture is the more expensive coffee.
ANSWER: 7/10 of 25 pounds, or 17.5 pounds, of the more expensive coffee; the other 7.5 pounds of the less expensive.
You can put this solution on YOUR website! ------------------------------------------------------------------
A coffee merchant combines coffee that costs $7 per pound with coffee that costs $3.30 per pound. How many pounds of each should be used to make 25 lb of a blend costing $5.89 per pound?
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$H, the more expensive priced coffee
$L, the lower priced coffee
M, how much of the blend to prepare
T, the expected price of the blend
w, the amount of the expensive coffee to use
Accounting for the cost of the blend,
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Substitute the values given in your description. The fraction part may be easy to compute. w can be calculated and then M-w can be evaluated.
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