The number of students that will need to buy the tickets is 419.
The equation that can be formed from the information provided in the question is:
$20s < $1250 + $625 + $1470 + $12s
Where s represents the number of students
$20s < $3345 + $12s
$20 - $12s < $3345
$8s < $3345
s < $3345 / $8
s < 419
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