The average height of 49 students in a class is 170 cm. If a boy is replaced by two boys whose average height is 180 cm, the average height of the class remains the same. Find the height of the boy who was replaced.

Since the average remains 170 cm for the new total of 50 students, the total height must be 50 times 170, equaling 8500 cm. Let the replaced boy's height be x, so the original total height was 8500 minus the sum of the two new boys. The two new boys have a combined height of 2 times 180, equaling 360 cm. Setting 8500 minus 360 equal to x plus 49 times 170 gives 8140 equals x plus 8330, solving to x equals 190 cm.

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