Question

You want to make a 1-ton ration of a 20% protein ration using corn (16%) and soybean meal (26%). How much of each will he have to mix together? Show your work for full credit.

Answer 1

To create a 1-ton ration of a 20% protein mixture, you need 1200 pounds of corn (16% protein) and 800 pounds of soybean meal (26% protein).

Step-by-step explanation:

We want to create a 1-ton ration of a 20% protein mixture using corn (16% protein) and soybean meal (26% protein). To solve this problem, we will use the method of linear equations to find out how much of each ingredient is needed.

Step 1: Determine Total Weight

Since 1 ton is equal to 2000 pounds, we need a total of 2000 pounds of mixture.

Step 2: Set Up Equations

Let x be the amount of corn needed and y be the amount of soybean meal needed.

For total weight: x + y = 2000

For protein content: 0.16x + 0.26y = 0.20(2000)

Step 3: Solve Equations

Using the first equation to solve for y we get y = 2000 - x. Substitute this into the second equation and solve for x:

0.16x + 0.26(2000 - x) = 400

Simplify the equation and solve for x:

x = (0.26*2000 - 400) / (0.26 - 0.16)

x = 1200 pounds of corn

Now solve for y using y = 2000 - x:

y = 2000 - 1200

y = 800 pounds of soybean meal

Therefore, the student must mix 1200 pounds of corn with 800 pounds of soybean meal to make a 1-ton ration of 20% protein mixture.