a farm supply company in franklin county has developed its own blend of grains for horses. the blend…

a farm supply company in franklin county has developed its own blend of grains for horses. the blend includes oats, which cost $9.40 per kilogram, and feed corn, which costs $3.40 per kilogram. overall, the mixture costs $5.80 per kilogram. if a worker at the company is mixing up a batch and starts with 130 kilograms of oats, how many kilograms of corn should he add to make the blend? write your answer as a whole number or as a decimal rounded to the nearest tenth. kilograms

a farm supply company in franklin county has developed its own blend of grains for horses. the blend includes oats, which cost $9.40 per kilogram, and feed corn, which costs $3.40 per kilogram. overall, the mixture costs $5.80 per kilogram. if a worker at the company is mixing up a batch and starts with 130 kilograms of oats, how many kilograms of corn should he add to make the blend? write your answer as a whole number or as a decimal rounded to the nearest tenth. kilograms

Answer

Answer:

260.0

Explanation:

Step1: Set up the equation

Let $x$ be the kilograms of corn. The cost - equation based on the weighted - average is $9.40\times130 + 3.40x=5.80\times(130 + x)$.

Step2: Expand the equation

$1222+3.40x = 754+5.80x$.

Step3: Move the $x$ terms to one side

$5.80x - 3.40x=1222 - 754$.

Step4: Simplify both sides

$2.4x = 468$.

Step5: Solve for $x$

$x=\frac{468}{2.4}=195$.