Problema Solution
Abe has a bag of marbles and wants to divide them into sets. The first set will have 2 marbles; the second set, 5; the third set, 8; the fourth set, 11; and so on. How many sets will he have if he starts with 40 marbles?
Answer provided by our tutors
the 1st set has: 2
the 2nd set has: 2 + 3 = 5
the 3rd set has: 2 + 3*2 = 8
the 4th set has: 2 + 3*3 = 11
the n-th set has: 2 + (n - 1)3 = 3n - 1
Abe has 40 marbles means the sun:
2 + 5 + 6 + 11 + ...+3n - 1 <= 40
we need to find n
since 2 + 5 + 6 + 11 + 14 <= 38 we have
3n - 1 = 14
by solving we find:
n = 5 sets
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he will have 5 sets.