An animal feed to be mixed from soybean meal and oats must contain at least 120 lb of protein, 24 lb of fat, and 10 lb of mineral ash.

Each sack of soybeans costs $ 15 and contains 50 lb of protein, 8 lb of fat, and 5 lb of mineral ash.

Each sack of oats costs $5 and contains 15 lb of protein, 5 lb of fat, and 1 lb of mineral ash.

How many sacks of each should be used to satisfy the minimum requirements at minimum cost?

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

the answer is y < -3 or   y > 3

-3y > 7 + 2

-3 y > 9

y < -3

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x