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?

The number of high protein feeds needed is 37.5 pounds

Step-by-step explanation:

Firstly we define variables. Let the number of pounds of dog food be d and the number of pounds of protein feeds be p.

We have 50 pounds in total, this means:

d + p = 50 ... (I)

The total cost here would be 50 * $1.25 since it's $1.25 per pound: 1.25 * 50 = $62.5

Now, we multiply each feed by their cost to arrive at the total cost

This means that:

0.5d + 1.5p = 62.5 ... (ii)

We can rewrite i as d = 50 - p

We substitute this in ii

0.5 (50-p) + 1.5p = 62.5

25 - 0.5p + 1.5p = 62.5

P = 62.5 - 25 = 37.5 pounds