SOLUTION: 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 t

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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?
Answer by funmath(2933) About Me  (Show Source):
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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:
%282%2F3%29x%2B%281%2F4%29x%2B10=x life is to short to fight with fractions, so eliminate the fractions by multiplying everything by the LCD, 12:
12%282%2F3%29x%2B12%281%2F4%29x%2B12%2810%29=12%28x%29
%2812%2F3%29%282x%29%2B%2812%2F4%29x%2B120=12x
4%282x%29%2B3x%2B120=12x
8x%2B3x%2B120=12x
11x%2B120=12x
-11x%2B11x%2B120=12x-11x
120=x
The total distance of the trip: x=120 mi.
Happy Calculating!!!