A man sells a nut mixture consisting of 1/3 pecans and 2/3 cashews. Pecans cost 3 times as much as cashews. if a pund of the mixture costs him $0.40, how much did he pay for a pond of cashews? a pound of pecans?
the cost of a pound of pecans is p, so
(2/3)c + (1/3)(3c) = 0.40
5/3 c = .40
c = .24
so, cashes cost $0.24/lb
pecans cost $0.72/lb
To solve this problem, let's first assign variables to the cost of cashews and pecans. Let's say the cost of cashews is C dollars per pound, and the cost of pecans is P dollars per pound.
We know that the nut mixture consists of 1/3 pecans and 2/3 cashews. This means that for every pound of mixture, there are 1/3 pounds of pecans and 2/3 pounds of cashews.
The total cost of 1 pound of nut mixture is $0.40. Since the mixture contains 1/3 pounds of pecans and 2/3 pounds of cashews, we can set up the following equation:
(1/3)P + (2/3)C = $0.40
We also know that the cost of pecans is 3 times the cost of cashews, so we can write:
P = 3C
Now we have a system of two equations:
(1/3)P + (2/3)C = $0.40
P = 3C
To solve this system, we can substitute the value of P from the second equation into the first equation:
(1/3)(3C) + (2/3)C = $0.40
Simplifying the equation, we get:
C + (2/3)C = $0.40
(5/3)C = $0.40
C = ($0.40 * 3) / 5
C = $0.24
Therefore, the man paid $0.24 for a pound of cashews.
To find the cost of a pound of pecans, we can substitute the value of C back into the equation P = 3C:
P = 3 * $0.24
P = $0.72
So, the man paid $0.72 for a pound of pecans.