Question

When 120 candies are given to 25 children and the number of candies for each child is at most 7,

what is the maximum number of children who get only 1 candy?​

Answer 1

The equation would be x=y(25)+8x=y(25)+8

Next get x by itself in xx mod28=22mod28=22

The equation would be x=z(28)+22x=z(28)+22

Set the equations so they are equal, 25y+8=28z+2225y+8=28z+22

Then, 25y=28z+1425y=28z+14

25y=(2z+1)∗1425y=(2z+1)∗14

This is true iff y=14y=14 , and 2z+1=252z+1=25

Now solve z. 2z=242z=24

z=12z=12

Substituting. x=28(12)+22x=28(12)+22

x=336+22x=336+22

x=358x=358

So, the total number of candy is 358