Question 160573
Let x=amount of 40% peanuts needed
Then 10-x=amount of 10% peanuts needed

Amount of pure peanuts in the 40% mixture (0.40x) plus amount of pure peanuts in the 10% mixture ((0.10(10-x)) has to equal amount of pure peanuts in final mixture(0.25*10).  So, our equation to solve is:

0.40x+0.10(10-x)=0.25*10  get rid of parens

0.40x+1-0.10x=2.5  subtract 1 from each side
0.40x-0.10x+1-1=2.5-1  collect like terms
0.30x=1.5  divide each side by 0.30
x=5 lb----------------------------------amount of 40% peanuts needed
10-x=10-5=5 lb---------------amount of 10% peanuts needed

CK
0.40*5+0.10*5=0.25*10
2+0.5=2.5
2.5=2.5

Hope this helps---ptaylor