The three children in a family have feet that are 3 inches 5

The three children in a family have feet that are 3 inches, 5 inches, and 7 inches

long. When they measure the length of the dining room of their house using their

feet, they each find that there are 2 inches left over. How long is the dining room.

Solution

Let x be the length of the room.

So x is a multiple of 3 +2

Hence, x=2 mod 3

Similarly,x=2 mod 5

x=2 mod 7

By chinese remainder theorem solution exists to these three equations.

x=2 mod 5

x=5m+2 =2m+2 mod 3=2m-1 mod 3

We need x=2 mod 3

Hence, m must be 0 mod 3

So, m=3k

x=15k+2

2,17,32,47,52,67,82,97,112,127,142

So we observe first solution is:x=2 which is too small.

Next solution is:x=142

So, x must be 142 inches.