Cashew nuts are sold at 15 per kg. Walnuts are sold at 12 per kg. What quantities of each nut would a store owner put into a 100-kg barrel so that it could be sold for 13.20 per kg?
C+W=100
15C+12W=13.2*100
Can you take it from here?
To solve this problem, let's assume that 'x' represents the quantity (in kg) of cashew nuts, and 'y' represents the quantity (in kg) of walnuts.
We know that the store owner intends to fill a 100-kg barrel, so we have the equation:
x + y = 100
Additionally, we need to consider the price at which the barrel will be sold. To achieve an average price of $13.20 per kg, the value of the cashews and the walnuts combined should be equal to 100 kg multiplied by $13.20, which is $1320. Therefore, we have another equation:
15x + 12y = 1320
Now we have a system of equations:
x + y = 100
15x + 12y = 1320
We can solve this system of equations using various methods, such as substitution, elimination, or matrix algebra. Let's solve it using the substitution method:
From the first equation, we can rewrite it as x = 100 - y. We substitute this value for 'x' in the second equation:
15(100 - y) + 12y = 1320
1500 - 15y + 12y = 1320
-3y = 1320 - 1500
-3y = -180
y = (-180) / (-3)
y = 60
Now that we have the value of 'y' (the quantity of walnuts), we can substitute it back into one of the original equations to find 'x':
x + y = 100
x + 60 = 100
x = 100 - 60
x = 40
Hence, the store owner should put 40 kg of cashew nuts and 60 kg of walnuts into the 100-kg barrel to achieve an average price of $13.20 per kg.