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# help

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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?

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

Nov 4, 2019
#2
+109202
+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

Nov 4, 2019