Peanuts sell for $6.00 per pound and cashews sell for $11.00 per pound. A merchant wants to sell a mixture of peanuts and cashews.

Question

How many pounds of peanuts and cashews must be used to create 25 pounds of a mixture that will sell for $7.20 per pound?

The mixture must contain _______ pounds of peanuts.

The mixture must contain _______ pounds of cashews.

 

Answer 1

Hi Jordan, the best way to work this type of problem is to set up a table.

 

Type       Amount          Cost         Total

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

Peanuts         x             6.00          6.00x

 

Cashews   25 - x         11.00       11.00 * (25 - x)

 

Mixture        25            7.20          7.20 * 25

 

Peanuts + Cashews must equal Mixture

 

6.00x + 11.00 * (25 - x) = 7.20 * 25

 

Clear parenthesis and combine terms:

 

6.00x + 275 - 11.00x = 180

 

-5.00x = -95

 

x = 19

 

You need 19 pounds of peanuts.

 

You need 29 - 19, or 6 pounds of cashews.

 

Questions?