On the first day of vacation, you read one-quarter of a novel. on the second day, you read half of the remaining pages. on the third day, you read the last 108 pages of the novel. how many pages does the novel have? how many pages did you read by the end of the second day?

A] Let the total number of pages be x, this is equivalent to 1/1
The fraction of novel read on the first day is 1/4 
The remaining fraction of pages will be:
1/1-1/4=3/4
Fraction read on the second day:
1/2×3/4=3/8
The remaining fraction will be:
1-(3/8+1/4)
=1-5/8
=3/8
Thus the fraction read on the third day is 3/8:
therefore:
3/8 represents 108 hence:
x=(1/1)/(3/8)×108
x=288 pages

b] The number of pages read on the second day will be:
(total number of pages)×(fraction of pages read on the second day)
total number of pages=288
fraction read on the second day=3/8
hence number of pages read on this date will be:

=288×3/8
=108

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12