Question 1021147: Eight girls arrived at Lucy's party. During the party, Lucy passed around a jar of candies. The first girl took a candy, the second girl took 3 candies, the third girl took 5 candies and so on. After the last took her candies, the jar was empty. Before the party started, Lucy ate 5 candies from the jar and gave a friend 3. How many candies were in the jar at first?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 8 girls at the party.
first girl took 1
second girl took 3
third girl took 5
each succeeding girl took 2 more than the previous girl took.
before the party started, lucy ate 5 and gave a friend 3.
there were 8 missing from the jar when the party started.
if the first girl took 1 and each succeeding girl took 2 more than that, then you have an arithmetic sequence where An = A1 + (n-1)*2.
if n = 8, and A1 = 1, then you have A8 = 1 + 7*2 = 1 + 14 = 15.
the eighth girl took 15 candies out of the jar.
the sum of an arithmetic series is Sn = n/2 * (A1 + An)
when n = 8, you get S8 = 8/2 * (A1 + A8)
since A1 = 1 and A8 = 15, you get S8 = 8/2 * (1 + 15) which results in S8 = 8/2 * 16.
S8 is equal to 8/2 * 16 which is equal to 8 * 8 which is equal to 64.
the 8 girls took out a total of 64 candies.
add the 8 that lucy ate and her friend took, and you get 72 candies were originally in the jar.
to confirm:
start with 72.
subtract 5 that lucy ate and 3 that her friend ate to get 64.
first girl took 1 which left 63.
second girl took 3 which let 60.
third girl took 5 which left 55.
fourth girl took 7 which left 48.
fifth girl took 9 which left 39.
sixth girl took 11 which left 28.
seventh girl took 13 which left 15
eight girl took 15 which left 0.
your solution is that 72 candies were originally in the jar.
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