a mixture of peanuts and corn sells for P40 per kilo. The peanuts sell for P42 per kilo while the corn sells for P36 per kilo. how many kilos of each kind are used in 12 kilos of a mixture

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)

The cost of 1 kg of peanuts = $ 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) = 42 x + 36 y

x + y = 12 ⇒ y = 12 - x

Put this in 40 (x + y) = 42 x + 36 y

We get:

40 (x + 12 - x) = 42 x + 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