NutShoppe has 10 kg of mix cashews and pecans which sell for $8.40 / kg. cashews sell for $8 / kg and pecans sell for $9 / kg. how many kg of each are in mix

Question

This is in a "mixture problems" unit in my text book. thank you

Answer 1

Let C = kg of cashews

Let P = kg of pecans 

 

10 kg mix  ==>  C + P = 10  ==>  C = 10 - P

 

The total value of a mixture of C kg of cashews and P kg of pecans is 8*C + 9*P 

 

The total value of a 10 kg mix which sells for 8.40/kg is 10*8.4 = 84 

 

So 8*C + 9*P = 84 

 

Substitute the value for C from the 1st equation into this equation 

 

8*(10 - P) + 9*P = 84

80 - 8*P + 9*P = 84

P = 4

 

So C = 10 - 4 = 6 

 

There should be 6 kg of cashews and 4 kg of pecans in the mix 

 

Check:  (6 kg)*($8 / kg) + (4 kg)*($9 / kg) = $48 + $36 = $84 = $8.40 / kg for a 10 kg mix