yolanda sells two grades of dog food. type a sells for 75 cents per pound and type b sells for 52 cents per pound. how many pounds of each must be used to produce 600 pounds of mixture selling for 60 cents per pound?
if a lbs are type a, then the rest (600-a) are type b. So, add up the parts and make sure it matches the whole:
75a + 52(600-a) = 60*600
To solve this problem, we can use a system of equations. Let's assign variables to the amounts of each type of dog food:
Let x be the number of pounds of type A dog food.
Let y be the number of pounds of type B dog food.
According to the problem, we know three things:
1. The total weight of the mixture is 600 pounds, so we have the equation:
x + y = 600
2. The cost of type A dog food is 75 cents per pound, and the cost of type B dog food is 52 cents per pound. The final mixture costs 60 cents per pound, so we have the equation:
0.75x + 0.52y = 0.60(600)
We can solve this system of equations to find the values of x and y.
First, let's simplify the second equation:
0.75x + 0.52y = 360
Next, let's solve the first equation for one variable:
x = 600 - y
Now we can substitute x in the second equation:
0.75(600 - y) + 0.52y = 360
450 - 0.75y + 0.52y = 360
-0.23y = -90
y = -90 / -0.23
y ≈ 391.30
Now that we have the value of y, we can substitute it back into the first equation:
x + 391.30 = 600
x ≈ 600 - 391.30
x ≈ 208.70
Therefore, approximately 208.70 pounds of type A dog food and approximately 391.30 pounds of type B dog food should be used to produce 600 pounds of the mixture selling for 60 cents per pound.