Question

John has 3000 hogs. He developed a balanced ration of 14% crude protein using the following feedstuff:40% crude protein supplement at $12.50 per 50 pounds and corn with 8.6% crude protein at $4.75 per bushel.a.How many pounds of each feedstuff did she use per 100 pounds of ration?b. How much did a ton of the ration cost?c. How many kilograms are in 12000 pounds of the mix? (Note: 1 kg = 2.2 lbs.)

Answer 1

a. variables:

x: pounds of crude protein supplement

y: pounds of corn

40% of crude protein supplement is protein.

8.6% of corn is protein

14% of the balanced ration is protein

In 100 pounds of ration we get:

0.4x + 0.086y = 0.14*100

0.4x + 0.086y = 14 (eq. 1)

Also

x + y = 100 (eq. 2)

Isolating x from the second equation,

x = 100 - y

Replacing this result into the first equation,

0.4(100 - y) + 0.086y = 14

0.4*100 - 0.4y + 0.086y = 14

40 - 0.314y = 14

-0.314y = 14 - 40

y = (-26)/(-0.314)

y = 82.8

Then

x = 100 - 82.8

x = 17.2

There are 17.2 pounds of crude protein supplement and 82.8 pounds of corn in 100 pounds of ration

b. First, we need to compute how many pounds of each feedstuff is in 1 ton, using the next proportions:

`\begin{gathered} \frac{100\text{ lb}}{2000\text{ lb}}=\frac{17.2\text{ lb of supplement}}{x\text{ lb of supplement}} \\ 100\cdot x=17.2\cdot2000 \\ x=(17.2\cdot2000)/(100) \\ x=344\text{ lb of supplement} \end{gathered}`

`\begin{gathered} \frac{100\text{ lb}}{2000\text{ lb}}=\frac{82.8\text{ lb of corn}}{x\text{ lb of corn}} \\ x=(82.8\cdot2000)/(100) \\ x=1656\text{ lb of corn} \end{gathered}`

Protein supplement cost $12.50 per 50 pounds, then 344 lb cost: