Question

A dairy farmer wants to mix a 85% protein supplement and a standard 60% protein ration to make 1200 pounds of a high-grade 70% protein ration. How many pounds of each should he use?

Answer 1

• 85% protein supplement: 480 pounds

,

• 60% protein ration: 720 pounds

Explanation:

Let the number of pounds of 85% protein supplement required = x

The farmer wants to make 1200 pounds (of a high-grade 70% protein ration).

Therefore, the number of pounds of 60% protein ration required = (1200-x) lbs

First, we add the constituents we are mixing together.

`0.85x+0.6(1200-x)`

The final protein ration we want to obtain:

`1200*0.7`

Equate both:

`0.85x+0.6(1200-x)=1200*0.7`

Then solve the equation for x.

`\begin{gathered} 0.85x+720-0.6x=840 \\ 0.85x-0.6x=840-720 \\ 0.25x=120 \\ \implies x=(120)/(0.25) \\ x=480\text{ pounds} \end{gathered}`

The number of pounds of the 85% protein supplement he should use is 480 pounds.

`1200-x=1200-480=720\text{ pounds}`

The number of pounds of the 60% protein ration he should use is 720 pounds.