Question

A zookeeper needs to mix feed for the prairie dogs so that the feed has the right amount of protein. Feed A has 25%

protein. Feed B has 11% protein. How many pounds of each does he need to mix to get 60 lbs of feed that is 18%
protein?

Answer 1

To create 60 lbs of feed with 18% protein, the zookeeper must mix 30 lbs of Feed A (25% protein) with 30 lbs of Feed B (11% protein) by solving a system of equations.

Step-by-step explanation:

The student asked how many pounds of each type of feed, A and B, a zookeeper needs to mix to get 60 lbs of feed that is 18% protein. Feed A has 25% protein and Feed B has 11% protein. This is a problem of mixtures and concentrations, which can be solved using a system of equations.

Let's call the amount of Feed A that needs to be mixed x pounds and the amount of Feed B y pounds. We have two conditions:

1. The total weight of the mixture must be 60 pounds: x + y = 60.
2. The total percentage of protein in the mix must be 18%: 0.25x + 0.11y = 0.18 * 60.

So, we have our system of equations:

• x + y = 60
• 0.25x + 0.11y = 10.8

Multiplying the second equation by 100 to simplify the decimals, we have:

• x + y = 60
• 25x + 11y = 1080

Now, we can solve this system by substitution or elimination. Let's use substitution:

• From the first equation, y = 60 - x
• Substitute y in the second equation: 25x + 11(60 - x) = 1080

Which simplifies to:

• 25x + 660 - 11x = 1080
• 14x = 420
• x = 30

Now we substitute x back into the first equation to find y:

• y = 60 - 30
• y = 30

Therefore, the zookeeper needs to mix 30 lbs of Feed A with 30 lbs of Feed B to get 60 lbs of feed with 18% protein.