Question

You are feeding your horses a 25 lb ration of grain and hay. You feed a 14% grain and a 9% orchard grass hay. If you want an 11% protein diet, how many lbs of grain, and how many lbs of hay will you feed each day?

Answer 1

To achieve an 11% protein diet from a 25 lb ration of 14% protein grain and 9% protein hay, solve the two equations x + y = 25 and 0.14x + 0.09y = 2.75 simultaneously to find that you need 10 lbs of grain and 15 lbs of hay.

Step-by-step explanation:

To figure out how many pounds of grain and hay are needed to create an 11% protein diet from a 25 lb ration, while knowing that grain is 14% protein and orchard grass hay is 9% protein, we will use a system of equations. Let x represent the pounds of grain, and y represent the pounds of hay. Therefore, the total weight of the ration implies that x + y = 25. To meet the desired protein percentage, we use the protein content of each feed to form the second equation: 0.14x + 0.09y = 0.11 * 25.

Now we have two equations:

1. x + y = 25
2. 0.14x + 0.09y = 2.75

Solving these simultaneously gives us the weights for grain and hay. From the first equation, we can express y in terms of x: y = 25 - x. Substituting this into the second equation gives us: 0.14x + 0.09(25 - x) = 2.75, which simplifies to 0.14x + 2.25 - 0.09x = 2.75, and further to 0.05x = 0.5. Thus, x = 10 pounds of grain and y = 25 - x = 15 pounds of hay.