Rachel has 42 blank audio cassettes, all of which are either 60 or 90 minutes long. If Rachel has less than 57 hours total of blank tape, how many 90 minutes tapes does she have?

Can you please help me with this problem? Me and my dad worked on it for about 25 minutes today:) and we never got the answer they wanted. If you would like, I can show you the work that we did. Thanks!

First, convert everything to hours. The cassettes are either 1 or 1.5 hours long. Say the number of long cassettes is x and the number of short ones is y.

x + y = 42
1.5x + 1y < 57

Substitute:

y = 42 – x
1.5x + (42 – x) < 57
0.5x + 42 < 57
0.5x < 15
x < 30