ANSWER
10 cashews and 40 peanuts
EXPLANATION
Let the amount of pounds of cashews be c.
Let the amount of pounds of peanuts be p.
We have that 50 pounds of cashews and peanuts were mixed, so:
c + p = 50 _____(1)
Cashews cost $0.60 per pound and Peanuts cost $0.50 per pound.
50 pounds of cashews and peanuts are worth $0.52 per pound. So, this means that:
0.60 * c + 0.50 * p = 0.52 * 50
=> 0.6c + 0.5p = 26 _____(2)
We now have a system of simultaneous equations:
c + p = 50 _____(1)
0.6c + 0.5p = 26 _____(2)
From (1):
c = 50 - p
Put that in (2):
0.6(50 - p) + 0.5p = 26
30 - 0.6p + 0.5p = 26
Collect like terms:
-0.1p = 26 - 30 = -4
Divide through by -0.1:
p = -4 / -0.1
p = 40
Recall that:
c = 50 - p
c = 50 - 40
c = 10
Therefore, 10 cashews and 40 peanuts should be mixed.