I'm getting confused from the wording of this problem, and it's really bothering me. Can anyone help? A list showing the results of a race was posted. There were no ties among the runners. One runner realized that 13 more runners had finished after her than had finished before her. She also realized that the total number of runners was 4 times the number of runners who had finished before her. How many runners took part in the race?
Let runners that finished before her be x. Total runners = 4x + 1 (her) = x + x + 13 + 1 Therefore, 2x = 14 x = 7 Total runners = 4(7) + 1 = 29. Is that right?
I'm assuming you're taking algebra. Here's what they're asking: There are x runners in the race. A particular runner finished with 14 runners behind her and x/4 runners ahead of her. That means that x=15+x/4 Multiply both sides by 4 and you get 4x=60+x Subtract x from both side, and you get: 3x=60 Divide by 3 on both sides x=20 She arrived in 6th place, BTW
If she finished in 6th, that would mean 5 people finished before her. Meaning 18 people finished AFTER her. 18 plus 6 does not equal 20 If she was in 8th, that would mean 7 people finished before her. Meaning 20 people finished AFTER her. 20 plus 8 DOES equal 28. Total participants is 28.
Yeah I got 28, thanks everyone! I did something like x = before y = after x - 13 = y x + y + 1 = 4y x = y + 13 so y + 13 + y + 1 = 4y 2y + 14 = 4y 14 = 2y y = 7 7 * 4 = 28
