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.
Algebra ->
Finance
-> 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.
Log On
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?
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 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?
===========================================================
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.
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.
(