A racing team needs $100-$octane fuel to safely run their car in an upcoming race, however, they can only get gasoline which has an octane rating of $93.$ As an octane booster, they use xylene $((C{H}_3{)}_2{C}_6{H}_4),$ which has an octane rating of $117$ and a density of ${}_{\text{x}\text{y}\text{l}\text{e}\text{n}\text{e}}=0\mathrm{.}864\frac{g}{mL}.$ In a mixing tank, they add $120$ gallons of the $93-$octane gasoline to $50$ gallons of xylene to bring their rating to the required $100-$octane.

Given:

$1$ gallon $93$ octane $=6\mathrm{.}05lbs$

$1$ gallon $89$ octane $=6\mathrm{.}2lbs$

$1kg=2\mathrm{.}205lbs$

$1$ liter $=0\mathrm{.}264$ gallons

$1$ newton $=1\frac{kg*m}{se{c}^2}$

$1$ lbs $=4\mathrm{.}4482$ newtons

What is the density of the $93-$octane gasoline $(\frac{g}{mL})?$

What is the mass $(kg)$ of the $93-$octane gasoline added to the tank?

What is the mass $(kg)$ of the xylene added to the tank?

What is the mass fraction of the gasoline in the tank?

What is the final density of the $100-$octane racing fuel?