Answer:
The weight of peanuts in the mixture  = 8  kg
The weight of corns in the given mixture = 4 kg
Step-by-step explanation:
Let us assume the weight of peanuts in the mixture  = x kg
The weight if corns in the given mixture = y kg
Total weight = (x + y) kg
The combined mixture weight = 12 kg
⇒ x  + y = 12  ..... (1)
Cost of per kg if mixture  = $ 40
So, the cost of (x + y) kg mixture  = (x+y) 40 = 40(x+ y)  ..... (2)
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The cost of 1 kg of peanuts = Â $ 42
So cost of x kg of peanuts  = 42 (x)  = 42 x
The cost of 1 kg of corns  = $ 36
So cost of y kg of corns  = 36 (y)  = 36 y
So, the total cost of x kg peanuts  + y kg corns =  42 x +  36 y  .... (3)
From (1) and (2), we get:
40(x+ y) Â = 42 x + Â 36 y
x +  y = 12 ⇒ y = 12 -x
Put this in  40(x+ y)  = 42 x +  36 y
We get:
40(x+ 12 -x) Â = 42 x + Â 36 (12 -x)
480 = 42 x + 432 - 36 x
or, 480 - 432 = 6 x
or, x  = 8
⇒ y = 12 -x = 12 - 8 = 4
⇒  y = 4
Hence, the weight of peanuts in the mixture  = 8  kg
The weight of corns in the given mixture = 4 kg
