How many peanuts should be mix w/ a nut mixture that is 40%peanuts to produce 36ounces of a 60%peanut mixture

balance the weight of peanuts

let there be x ounces of the 40% nut mixture ==> .40x ounces of peanuts

since there are 36 ounces of the final mixture, there must be 36 - x ounces of pure peanuts

36 ounces of 60% mixture ==> .60(36) = 21.6 ounces of peanuts

these must balance:

.40x + (36 - x) = 21.6
36 - 21.6 = x - .40x
14.4 = .60x
14.4 / .6 = x
24 = x

24 ounces of 40% mixture
12 ounces of pure peanuts

total: 36ounces of 60% mixture

check:
.4 (24) = 9.6

12 + 9.6 = 21.6, the amount of peanuts in 36 ounces of 60% mixture

P+0.4N=0.6*36 = 21.6
P+N=36 subtract equations
0.6N=14.4
N = 24
P=12
!2 oz of peanuts needs to be added