SOLUTION: Can you please help me solve this word problem? A group of runners participated I a 10-kilometer race. One-eighth of the runners completed the race in 40 minutes or less. Seven

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Can you please help me solve this word problem? A group of runners participated I a 10-kilometer race. One-eighth of the runners completed the race in 40 minutes or less. Seven      Log On


   

Question 640803: Can you please help me solve this word problem?
A group of runners participated I a 10-kilometer race. One-eighth of the runners completed the race in 40 minutes or less. Seven-Twelfths of the runners needed between 40 minutes and one hour to complete the race. The remaining 70 runners took one hour or longer to complete the race. How many runners completed the race?
I already tried to solve this a few time but I keep getting confused. So far I did 1/8+ 7/12+ 70 =x
Then, 3/24+14/24+70=x
Next, 17/24+70=x
Finally, 70 and 17/24=x
This is incorrect because you cannot have 17/24 of a person and there are more than 70 people in the race, obviously.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
For short, I'm calling runners only those who completed the race.
(I mean no offense to those who could not finish for whatever reason).
1%2F8 of the total number of runners + 7%2F12 of the total number of runners + 70 runners = confusion
You were adding apples and oranges, or fractions of an unknown number plus the known number 70.
Let x be the total number of runners.
One eight of the total number of runners is %281%2F8%29x.
Seven-twelfths of the total number of runners is %287%2F12%29x.
%281%2F8%29x%2B%287%2F12%29x%2B70=x
Multiplying both sides of the equation times 24,
24%28%281%2F8%29x%2B%287%2F12%29x%2B70%29=24x
24%281%2F8%29x%2B24%287%2F12%29x%2B24%2A70=24x
3x%2B14x%2B1680=24x
17x%2B1680=24x
17x%2B1680-17x=24x-17x
1680=7x
1680%2F7=7x%2F7
240=x or highlight%28x=240%29.
So, highlight%28240%29 people completed the race.