Question 56700
Going to Austin, Bill caught a ride for two-third of the total distance with a friend.  He then took a bus for one-fourth of the total distance.  He walked the remaining 10 miles to arrive at his destination.  What was total distance of his destination?
Let the total distance: x
Then he caught a ride with a friend for: (2/3)x
He rode a bus for: (1/4)x
He walked for: 10 mi.
The equation to solve:
{{{(2/3)x+(1/4)x+10=x}}}  life is to short to fight with fractions, so eliminate the fractions by multiplying everything by the LCD, 12:
{{{12(2/3)x+12(1/4)x+12(10)=12(x)}}}
{{{(12/3)(2x)+(12/4)x+120=12x}}}
{{{4(2x)+3x+120=12x}}}
{{{8x+3x+120=12x}}}
{{{11x+120=12x}}}
{{{-11x+11x+120=12x-11x}}}
{{{120=x}}}
The total distance of the trip: x=120 mi.
Happy Calculating!!!