help me please

Question

i have 15 pounds of organic almonds, which cost $13.50 per pound, i want to mix the almonds with organic cashews, which cost $10.50 per pound, to create a mixture worth $12.50 per pound. how many pounds of cashews should i include in my mix?

Answer 1

Let C = pounds of cashews  

Then total pounds in mixture = 15 + C  

 

The total value of 15 pounds of almonds plus C pounds of cashews is 15*13.50 + C*10.50  

 

This must equal the total value of the mixture which is (15 + C)*12.50, so  

 

15*13.50 + C*10.50 = (15 + C)*12.50

202.50 + 10.50*C = 187.50 + 12.50*C

15 = 2*C

C = 7.5 pounds of cashews  

 

Check:  15*13.50 + 7.5*10.50 = 202.50 + 78.75 = $281.25  

            (15 + 7.5)*12.50 = 22.5*12.50 = $281.25