pre calc word problem

Question

A coffee house blended 6 pounds of espresso flavored coffee beans with 5 pounds of vanilla flavored coffee beans. The 11 pound mixture cost $77.50. A second mixture included 20 pounds of espresso flavored coffee beans and 13 pounds of vanilla flavored coffee beans. The 33 pound mixture cost $234.50. Find the cost per pound of the vanilla flavored coffee beans.

Answer 1

Use systems of equations to solve.

Let x represent the cost per pound of the espresso coffee beans and 

      y represent the cost per pound of the vanilla coffee beans.

1. 6x + 5y = 77.50
2. 20x + 13y = 234.50,  both of these are given.

 

Rewrite these equations so you can eliminate one of the variables;

1. 60x + 50y = 775,   Multiply both sides of the equation by 10
2. 60x + 39y = 703.5, Multiply both sides of the equation by 3

Now Subtract equation 2 from equation 1,

11y = 71.5

    y = 6.5

 

Solve for x, 

1. 6x + 5(6.50)= 77.50  

           x = 7.50

Therefore, the cost per pound of the espresso coffee beans is $7.50, and 

                the cost per pound of the vanilla coffee beans is $6.50.