Question 112547
Let x = number of gallons in the tank when full.


You begin with 1/8 of the full tank, you add 15 gallons, and what you have is 3/4 of a full tank.  So where x represents the "full tank", the equation is

{{{(1/8)*x + 15= (3/4)*x }}}


Multiply both sides of the equation by the LCD, which is 8:
{{{8*(1/8)*x + 8*15= 8*(3/4)*x }}}
{{{x + 120= 6x }}}
{{{120=5x}}}
{{{x=120/5= 24}}} gallons


Since you ended up with 3/4 of a tank, you have 3/4 of 24 which is 18 gallons in the car.  It will take 6 gallons to fill it the rest of the way.


Pretty neat problem!!


R^2