In audition for school play, 70% passed the quality of the jurors for the first week. of those remaining, 20% were chosen. if only 7 were qualified, how many tried their luck?
Let total number who tried out be X.
0.7 X * 0.2 = 7
X = 7/0.14 = 50
50
To find out how many people tried their luck in the audition, we need to work backwards from the given information.
Let's assume the total number of people who tried their luck is "x".
In the first week, 70% of the total number of people passed the quality of the jurors. So, the number of people who passed in the first week is 70% of "x", which is 0.7x.
Now, we know that "x" people tried their luck, but only 70% of them passed. Therefore, the number of people who didn't pass in the first week is the remaining 30% of "x", which is 0.3x.
Out of those who didn't pass the first week, only 20% were chosen. So, the number of people chosen from the remaining group is 20% of 0.3x, which is 0.2(0.3x) = 0.06x.
It is given that only 7 people qualified overall. So, the sum of the people who passed in the first week (0.7x) and the people chosen from the remaining group (0.06x) equals 7:
0.7x + 0.06x = 7
Combining like terms, we get:
0.76x = 7
Dividing both sides by 0.76, we find:
x = 7 / 0.76 ≈ 9.21
Therefore, approximately 9 or 9 people tried their luck in the audition.