SOLUTION: Light roast coffee beans cost seven dollars/pound, while dark roast cost $5.50 per pound. How much of each type of coffee is needed to create 4.50 pounds of a mixture that cost $6.

Question 1201904: Light roast coffee beans cost seven dollars/pound, while dark roast cost $5.50 per pound. How much of each type of coffee is needed to create 4.50 pounds of a mixture that cost $6.75 per pound?
Found 3 solutions by mananth, josgarithmetic, greenestamps:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
Light roast coffee beans cost seven dollars/pound, while dark roast cost $5.50 per pound. How much of each type of coffee is needed to create 4.50 pounds of a mixture that cost $6.75 per pound?

Light roast coffee beans cost seven dollars/pound let this be x lbs
dark roast cost $5.50 per pound ....(4.5-x)lbs
4.50 pounds of a mixture that cost $6.75 per pound?

Cost equation
7x+5.5(4.5-x) = 4.5*6.75 (mixture cost)
7x+24.75-5.5x=30.375
1.5x =5.625
x=3.75 lbs Light roast coffee beans
dark roast coffee beans= balance = 0.75 lbs

7.3.75+0.75*5.5 30.375 $

Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!
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Light roast coffee beans cost seven dollars/pound, while dark roast cost $5.50 per pound. How much of each type of
coffee is needed to create 4.50 pounds of a mixture that cost $6.75 per pound?
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Light roast coffee beans cost H dollars/pound, while dark roast cost $L per pound. How much of each type of
coffee is needed to create M pounds of a mixture that cost $T per pound?
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If amount of the higher priced material is v, then the amount of the lower priced material is M-v.

Substitute your values to find the numeric values you want.
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

I would strongly recommend against using the "magic" formula that tutor @josgarithmetic likes to show whenever they respond to a mixture problem like this. Blindly using the formula does not teach the student anything about how to solve the problem; and it is an ugly formula that is both hard to learn and hard to use correctly.

For a typical formal algebraic solution, look at the response from the other tutor.

And if formal algebra is not required, here is a quick and easy informal (and easy to understand) way to solve any 2-part mixture problem like this.

(1) Using a number line (if it helps), determine that the $6.75 cost per pound of the mixture is 5/6 of the way from $5.50 to $7.00.

(2) That means 5/6 of the mixture is the more expensive coffee beans.

Then use simple arithmetic to determine that 5/6 of 4.5 pounds is 3.75 pounds, so...

ANSWER: 3.75 pounds of the light roast coffee; 0.75 pounds of the dark roast.

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