There are 216 couples competing in a dance contest.After each half hour one-third of the contest-ants are eliminated. How many couples will remain eligible for the prize after the first hour?
a. 24
b. 46
c. 48
d. 96
e. 98
please answer and explain
After a half hour a third will go..
216x1/3=72 (go)
216-72=144 remaining after half hour
From the remaining 144, another third will go
144x1/3=48 (go in the second half hour=after an hour)
144-48=96 (left after an hour)
Therefore answer is d -96
The question asks how many remain after the first hour.
216/3 = 72
72/3 = 24
To find the number of couples that will remain eligible for the prize after the first hour, we need to calculate the number of couples eliminated at the end of each half hour and subtract it from the initial number of couples.
At the end of the first half hour, one-third of the couples are eliminated. Since there are 216 couples, we can find the number eliminated by multiplying 216 by one-third:
Number eliminated = 216 * (1/3) = 72 couples
Therefore, after the first half hour, there will be 216 - 72 = 144 couples remaining.
At the end of the second half hour, another one-third of the remaining couples will be eliminated. We can calculate this by multiplying the remaining couples (144) by one-third:
Number eliminated = 144 * (1/3) = 48 couples
So, after the second half hour, there will be 144 - 48 = 96 couples remaining.
Since the question asks for the number of couples remaining eligible for the prize after the first hour, the correct answer is (d) 96.