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# Alicia has \$n\$ candies, where \$n\$ is a positive integer with three digits. If she buys \$5\$ more, she will have a multiple of \$8\$. If she los

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Alicia has \$n\$ candies, where \$n\$ is a positive integer with three digits. If she buys \$5\$ more, she will have a multiple of \$8\$. If she loses \$8\$, she will have a multiple of \$5\$. What is the smallest possible value of \$n\$?

RektTheNoob  Sep 2, 2017
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#1
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123 + 5 = 128 multiple of 8

123 - 8 = 115 multiple of 5

Guest Sep 2, 2017
#2
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8 - 5 = 3

LCM (5, 8) = 40

(n + 5) mod 8 = 0

(n - 8) mod 5 = 0 , solve for n

n = 40D + 3,  for D=0, 1, 2, 3......etc. Since n must the smallest positive 3-digit integer, then we have:

n = 40*3 + 3

n = 120 + 3

n = 123

Guest Sep 3, 2017

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