Five chickens and eight turkeys cost $58.60. Three chickens and 4 turkeys cost $32.40. Find the cost of 7 chickens and 4 turkeys.
Let's assign variables to represent the unknown quantities:
Let x be the cost of one chicken.
Let y be the cost of one turkey.
From the given information, we can set up a system of equations:
Equation 1: 5x + 8y = 58.60
Equation 2: 3x + 4y = 32.40
We can solve this system of equations using the method of elimination.
Multiply equation 1 by 3 and equation 2 by 5 to make the coefficients of x in both equations to be the same:
15x + 24y = 175.80
15x + 20y = 162.00
Next, subtract equation 2 from equation 1 to eliminate x:
(15x + 24y) - (15x + 20y) = 175.80 - 162.00
15x + 24y - 15x - 20y = 13.80
4y = 13.80
y = 13.80/4
y = $3.45
Now that we know the cost of one turkey, we can substitute this value into equation 1 to solve for x:
5x + 8(3.45) = 58.60
5x + 27.60 = 58.60
5x = 58.60 - 27.60
5x = 31.00
x = 31.00/5
x = $6.20
Therefore, the cost of one chicken is $6.20 and the cost of one turkey is $3.45.
To find the cost of 7 chickens and 4 turkeys, we can substitute these values into equation 1:
7($6.20) + 4($3.45) = $43.40 + $13.80 = $57.20
So, the cost of 7 chickens and 4 turkeys is $57.20. Answer: \boxed{57.20}.