Cashew nuts sell for $21.00/kg. Brazil nuts sell for $15.00/kg. a distributed sold at total of 120kg of cashew and Brazil nuts for 2244 dollars. What mass of each type of nut was sold?
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To find the mass of each type of nut sold, we can set up a system of equations based on the given information.
Let's consider the mass of cashew nuts sold as x kg and the mass of Brazil nuts sold as y kg.
According to the given information, the price per kilogram of cashew nuts is $21.00/kg. Therefore, the total cost of cashew nuts sold would be 21x dollars.
Similarly, the price per kilogram of Brazil nuts is $15.00/kg. So, the total cost of Brazil nuts sold would be 15y dollars.
We are also given that the total cost of all the nuts sold is $2244. Therefore, the equation representing this information is:
21x + 15y = 2244 ----(1)
Additionally, the total mass of nuts sold is 120 kg. Thus, we have another equation based on the total mass:
x + y = 120 ----(2)
Now, we have a system of two linear equations:
21x + 15y = 2244 ----(1)
x + y = 120 ----(2)
We can solve this system of equations to find the values of x and y. One way to solve it is by the method of substitution.
From equation (2), we can rearrange it as x = 120 - y and substitute this expression into equation (1):
21(120 - y) + 15y = 2244
Now, simplify and solve for y:
2520 - 21y + 15y = 2244
-6y = 2244 - 2520
-6y = -276
y = (-276) / (-6)
y = 46
Now that we have found the value of y, we can substitute it back into equation (2) to find the value of x:
x + 46 = 120
x = 120 - 46
x = 74
So, the mass of cashew nuts sold was 74 kg, and the mass of Brazil nuts sold was 46 kg.