Question

A feedlot in Adams County has developed its own blend of grains for horses. The blendincludes oats, which cost $9.80 per kilogram, and feed corn, which costs $4.30 per kilogram.Overall, the mixture costs $8.15 per kilogram. If a worker at the feedlot is mixing up a batchand starts with 270 kilograms of oats, how many kilograms of corn should he add to makethe blend?Write your answer as a whole number or as a decimal rounded to the nearest tenth.

Answer 1

EXPLANATION

Let's call x to the oats and y to the corns.

Let's see the facts:

x= oats ----> $9.80/Kg

y= corns ---> $4.30/Kg

If the mixture cost is $8.15/ Kg, and the workers starts with 270 kilograms of oats, the kilograms of corn would be given by the following relationship:

The total cost of the oats is:

9.8*270 = 279.8 dollars

The total mixing amount is:

270 + y = z

The total cost equation is as follows:

8.15.z= 9.8*270 + 4.3*y

Replacing z= y + 270:

8.15(270+y) = 9.8*270 + 4.3y

Applying the distributive property:

2200.5 + 8.15y = 2646 + 4.3y

Subtracting 2200.5 to both sides:

8.15y = 2646 - 2200.5 + 4.3y

Subtracting 4.3y to both sides:

8.15y - 4.3y = 2646 - 2200.5

Simplifying like terms:

3.85y = 445.5

Dividing both sides by 3.85:

y= 445.5/3.85

Simplifying:

y = 115.71

The worker should add 116 kilograms of corns.