Jax bought exactly enough trees to plant eight equal rows. Then one tree died and couldn’t be planted, but he still had enough trees left to plant exactly nine equal rows. After that, a tree was stolen, but he still had enough trees left to plant exactly ten equal rows. If he bought the least number of trees satisfying these three conditions, how many trees did he buy?

Guest Nov 4, 2019

#1**+1 **

n mod 8 =0

n mod 9 =1

n mod 10 =2

The LCM of 8/2, 9, 10/2 =180

Using "Chinese Remainder Theorem + Modular Multiplicative Inverse"

180 + 172 = 352 minimum number of trees

Guest Nov 4, 2019

#2**+1 **

8 * A = 9 * B + 1 = 10 * C + 2

So.....

8A - 1 = 10C + 1

8A - 10C = 2

4A - 5C = 1

A C B

4 3 Not an integer

9 7 Not an integer

14 11 Not an integer

19 15 Not an integer

24 19 Not an integer

29 23 Not an integer

34 27 Not an integer

39 31 Not an integer

44 35 39

So he orginally has 8 rows * 44 per row = 352 trees

When he loses one he has 9 rows * 39 per row = 351 trees

Ad when he loses two he has 10 rows * 35 per row = 350 trees

CPhill Nov 4, 2019