# Trees

Loggers wanted to seed more than 700 and less than 800 trees. If they seed in rows of 37, left them 8 trees. If they seed in rows of 43, left the 11 trees. How many trees must seed ?

Correct result:

x =  785

#### Solution:

$700 < x < 800 \ \\ 700-8 < 37r < 800-8 \ \\ 692< 37r < 792 \ \\ 18 < r < 22 \ \\ \ \\ 700-11 < 43s < 800-11 \ \\ 689< 43s < 789 \ \\ 16 < s < 19 \ \\ \ \\ r = 19; x = 19\cdot 37+8 = 711 \ \\ r = 20; x = 20\cdot 37+8 = 748 \ \\ r = 21; x = 21\cdot 37+8 = 785 \ \\ \ \\ s = 17; x = 17\cdot 43+11 = 742 \ \\ s = 18; x = 18\cdot 43+11 = 785 \ \\ \ \\ \ \\ x = 785$

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