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

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)   (Show Source): You can put this solution on YOUR website!
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)   (Show Source): You can put this solution on YOUR website!
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.

Found 73 gumdrops.

Found 73 gumdrops.

Same way with divisor 6.

BUT,

Found 71 gumdrops.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

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
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