Chapter 6.3, Problem 16P

You drive a car that runs on ethanol and gas. You have a 20-gallon tank to fill and you can buy fuel that is either 25 percent ethanol or 85 percent ethanol. How much of each type of fuel should you buy to fill your tank so that it is 50 percent ethanol?

To determine

how much of each type of fuel have to buy in order to fill the tank

Answer to Problem 16P

  $25\%$ Ethanol $x\approx 11.67galoons$

  $85\%$ Ethanol $y\approx 8.33galoons$

Explanation of Solution

Given information:

20 gallon of tank is to be filled and it is possible to buy fuel of either 25 percent ethanol or 85 percent ethanol.

Calculation:

Assume x is the amount of $25\%$ ethanol fuel and y is the amount of $85\%$ ethanol fuel

Plotting the equation as below:

There are total of 20 gallons

  $X+Y=\mathrm{20.......}(1)$

Converting it into percentage it would be $50\%$ :

  $\begin{array}{l}0.25x+0.85y=0.5(20)\\ 0.25x+0.85y=\mathrm{10.......}(2)\end{array}$

Multiply equation 2 by equation 4

  $x+3.4y=\mathrm{40.....}(3)$

Now subtract equation 1 and equation 3 in order to eliminate x as follows:

  $2.4y=20$

Dividing the above equation with 2.4

  $y=\frac{25}{3}\approx 8.33galoons$

Solving for x using equation 1

  $\begin{array}{l}x+\frac{25}{3}\approx 20\\ x=\frac{35}{3}\approx 11.67\end{array}$

Conclusion:

  $25\%$ Ethanol $x\approx 11.67galoons$

  $85\%$ Ethanol $y\approx 8.33galoons$