A coffee company wants a new flavor of Cajun coffee.

Question

How many pounds of coffee worth $9 a pound should be added to 10 pounds of coffee worth $3 a pound to get a mixture  worth $7 a pound ?

Answer 1

Hi Charles, the best way to work mixture problems is to set up a table. Let x represent the amount of the $9.00 per pound coffee that must be added to make the mixture of $7.00 per pound coffee.

 

Table

 

Cost         Weight         Total

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

9                  x               9x

 

3                10               3*10

 

7              10 + x          7*(10 + x)

 

Equation:

 

9x + 3*10 = 7*(10 + x)

 

9x + 30 = 70 + 7x

 

Subtract 7x from both sides:

 

2x + 30 = 70

 

Subtract 30 from both sides:

 

2x = 40

 

Divide both sides by 2:

 

x = 20

 

The coffee company needs to add 20 pounds of coffee costing $9.00 per pound to 10 pounds of costing $3.00 per pound to get a mixture of coffee costing $7.00 per pound.

 

Questions?