SOLUTION: 1. larissa has a bag of gumdrops. she knows there are less than 75 pieces of candy in all. when she divides them into groups of 3,4,5,6 there is always 1 left over. how many gum

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Question 894180: 1. larissa has a bag of gumdrops. she knows there are less than 75 pieces of candy in all. when she divides them into groups of 3,4,5,6 there is always 1 left over. how many gumdrops does larissa have?
Found 3 solutions by richwmiller, josgarithmetic, MathTherapy:
Answer by richwmiller(17219) About Me  (Show Source):
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Either 1 or 61 gumdrops can be the answer.
If she gave out none to begin with the one is the answer
61 is divisible by 3,4,5,6 with one left over

Answer by josgarithmetic(39617) About Me  (Show Source):
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I tried this but found the divisor 5 was not consistent with the use of the other divisors.

Wanting remainder 1, this means 75-x divided by d must be some whole number PLUS 1/d.

%2875-x%29%2F3=24%2B1%2F3
Found 73 gumdrops.

%2875-x%29%2F4=18%2B1%2F4
Found 73 gumdrops.

Same way with divisor 6.

BUT,
%2875-x%29%2F5=14%2B1%2F5
Found 71 gumdrops.

Answer by MathTherapy(10552) About Me  (Show Source):
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1. larissa has a bag of gumdrops. she knows there are less than 75 pieces of candy in all. when she divides them into groups of 3,4,5,6 there is always 1 left over. how many gumdrops does larissa have?


LCM of 3, 4, 5, and 6: 60

Number of gumdrops: LCM, plus common remainder, or 60 + 1, or highlight_green%2861%29