Pcasey is reading a book for a book report. at 3: 30 p. m., he started reading where he had left off the day before. at 5: 30 p. m. he was on page 160. at 8: 00 p. m. he was on page 280. if reading the book is modeled by a linear function, what page did casey start on at 3: 30 p. m.?

Given:
3:30 - 5:30 = page 160
5:30 - 8:00 = page 280

280 - 160 = 120
8:00 - 5:30 = 2.5 hours or 5 half hours 
120 / 5 half hours  =  24 pages every half hour or 30 minutes

3:30 - 5:30 = 2 hours or 4 half hours
24 * 4 = 96 pages

160 - 96 = 64

P Casey was on page 64 at 3:30 p.m.

If you would like to know the page that Casey start on at 3:30 P.M., you can calculate this using the following steps:

8:00 P.M. - 5:30 P.M. = 2:30
280 - 160 = 120 pages

5:30 P.M. - 3:30 P.M. = 2:00

2:30 = 150 minutes ... 120 pages
2:00 = 120 minutes ... x pages = ?

150 * x = 120 * 120
x = 120 * 120 / 150
x = 96 pages

160 pages - 96 pages = 64

Casey started on page 64.