In a slalom skiing competition skiers tackle the course one at a time. Each skier makes two runs. The times for the two runs are added and the fastest total time determines the winner. Competitors who fail to finish their first run are not allowed to make a second run.
In the second round, skiers compete in the reverse order of their positions after the first round.
Grace took part in a slalom competition last week. She was the eighth skier to make her first run. At the end of the first round she was in sixth position, so she had to wait for 17 of her rivals to make their second runs before it was her turn again. Three skiers had failed to complete the course in the first round.
How many competitors took part in last week’s slalom competition?
Determine what they are trying to ask, and what you will need to solve it
Eliminate any non-essential information
Draw a picture, graph, or equation
In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.
Solve.
Approach: Sort through the useful and useless information. Then, for the second round, add the total skiers in front of her, skiers behind her, and finally, those who did not complete.
Useful:
She is in 6th after the first round.
There are 17 skiers before her in the second round.
The order in the second round is switched (the worst in the first round goes first in the second round)
3 skiers failed
Useless:
She was the 8th skier in the first round. This is not needed to solve the question because the first-round positions are not reflective of anything given in the question.
17 skiers before her in 2nd round + 6 (her and the 5 who finished before her since she’s 6th) + 3 who did not finish first round and won’t race again = 17 + 6 + 3 = 26
\fcolorbox{red}{grey!30}{Therefore the answer is A, there were $26$ total competitors.}