SOLUTION: Fred’s coffee shop makes a blend that is a mixture of two types of coffee. Type A coffee cost Fred $4.60 per pound, and type B coffee costs $5.70 per pound. This month’s blend

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Question 1195566: Fred’s coffee shop makes a blend that is a mixture of two types of coffee. Type A coffee cost Fred $4.60 per pound, and type B coffee costs $5.70 per pound. This month’s blend used twice as many pounds of type B as type A, for a total cost of $640.00. How many pounds of type A coffee were used?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
COFFEE       PRICE           QTY        COST
   A          4.60            a
   B          5.70           2a
blend                                   640.00


COFFEE       PRICE           QTY        COST
   A          4.60            a          4.6a
   B          5.70           2a         5.7*2a
blend                                   640.00








Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Fred’s coffee shop makes a blend that is a mixture of two types of coffee.
Type A coffee cost Fred $4.60 per pound, and type B coffee costs $5.70 per pound.
This month’s blend used twice as many pounds of type B as type A,
for a total cost of $640.00. How many pounds of type A coffee were used?
~~~~~~~~~~~~~~~~~~~~ 

Let  " a " be the pounds of the coffee type A.

Then the pounds of the coffee type B is 2a.


Write the total money equation

    4.60a + 5.70*(2a) = 640   dollars.


Simplify and find "a"

    (4.60 + 2*5.70)a = 640

         16a         = 640

           a         = 640/16 = 40.


ANSWER.  40 pounds of the coffee type A.


CHECK.  4.60*40 + 5.70*80 = 640.00  dollars, total.  ! Correct !

Solved.

---------------

Do not accept any other answer.

The solution and the answer of the other post  " 42 pounds "  is  INCORRECT.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The other two responses you have received show formal algebraic solutions.

If formal algebra is not required, you can solve this using logical reasoning and simple calculations. And doing that will give you good mental exercise.

The number of pounds of coffee of type B is twice the number of pounds of coffee of type A. So the cost of each 3 pounds of coffee is 2($5.70)+1($4.60)=$16; that makes the cost per pound of the mixture $16/3.

The total cost was $640, so the number of pounds of mixture was



Since the mixture was 120 pounds, 40 pounds were type A coffee and 80 pounds were type B coffee.

ANSWER: 40 pounds of type A coffee were used
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