Question

Dog food selling for $0.50 per pound is to be mixed with a high protein blend selling for $1.50 per pound. How many pounds of the high protein blend are needed to produce a 50 pound mixture that sells for $1.25 per pound.

Answer 1

To create a 50 pound mixture that sells for $1.25 per pound, it is necessary to mix 37.5 pounds of a high protein blend selling for $1.50 per pound with regular dog food selling for $0.50 per pound.

Step-by-step explanation:

To determine how many pounds of the high protein blend are needed for the mixture, we can use a system of equations based on the cost of each type of dog food.

We have two types of dog food:
1. Regular blend at $0.50 per pound
2. High protein blend at $1.50 per pound

We want to find the mixture that forms 50 pounds in total and sells for $1.25 per pound.

Let's denote the amount of regular blend as R and the amount of high protein blend as H. We have two equations:

1. R + H = 50 (the total weight of the mixture)
2. 0.50R + 1.50H = 50 * 1.25 (the total cost of the mixture)

From the first equation: R = 50 - H

Plug R into the second equation:
0.50(50 - H) + 1.50H = 62.50

Solve for H:

25 - 0.50H + 1.50H = 62.50
H = (62.50 - 25) / 1
H = 37.50 / 1
H = 37.5

So, 37.5 pounds of high protein blend are needed.

Answer 2

1

Step-by-step explanation: