Question

a fuel producer needs 960 gallons of fuel that contains 75% ethanol. to make this, the company will combine some 80%-ethanol fuel with some 55%-ethanol fuel. how much of each type should be used? write your answers as whole numbers or as decimals rounded to the nearest tenth. blank gallons of 80% fuel blank gallons of 55% fuel

Explanation:

Step1: Set up equations

Let \(x\) be the amount of \(80\%\) - ethanol fuel and \(y\) be the amount of \(55\%\) - ethanol fuel.
We have two equations:

1. \(x + y=960\) (total volume)
2. \(0.8x + 0.55y=0.75\times960\) (ethanol content)

From the first equation \(y = 960 - x\).

Step2: Substitute and solve

Substitute \(y = 960 - x\) into the second equation:

$$
LATEXBLOCK0
$$

Step3: Find \(y\)

Substitute \(x = 768\) into \(y=960 - x\)
\(y=960 - 768=192\)

Answer:

768 gallons of \(80\%\) fuel
192 gallons of \(55\%\) fuel