Since we know what time Dennis' sister finished babysitting, we can calculate how much money she's made since 9p.m. Between 9 and 11 is 2 hours, so we know she made $16 ($8 per hour x 2 hours).
That means she made $22 before 9p.m. ($32 total - $16 made past 9p.m.)
So, you just need to figure out how many hours $22 is worth and subtract that number of hours from 9p.m. That will get you to the starting point of babysitting.
$22 / $5.50 = 4 so we know that $22 is 4 hours' worth of babysitting.
9p.m. - 4 hours is 5p.m., so we know that Dennis' sister started babysitting at 5p.m.
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