Find the cost per pound of the peanuts and M&M's.

Question

A storeowner mixed 8 pounds of peanuts and 5 pounds of M&M's. This 13 pound mixture sold for $55.27. A second mixture included 6 pounds of peanuts and 4 pounds of M&M's. This 10 pound mixture sold for $42.70. Find the cost per pound of the peanuts and M&M's.

Answer 1

Let x = cost of one pound of peanuts

     y = cost of one pound of M&M's

 

Then, 8x + 5y = 55.27

         6x + 4y = 42.70

 

Multiply the first equation by 4 and the second equation by -5:

 

        32x + 20y = 221.08

       -30x  - 20y = -213.50

 

Adding the equations yields 2x = 7.58

 

                                         x = $3.79

 

Since x = 3.79 and 8x + 5y = 55.27, we get 8(3.79) + 5y = 55.27

 

                                                                            5y = 24.95

 

                                                                             y = $4.99

 

One pound of peanuts costs $3.79 and a pound of M&M's costs $4.99.