Assume that at the current exchange rate, the british pound is worth $1.65 in american dollars. you have some dollar bills and several british pound coins. there are 17 items altogether, which have a total value of $18.30 in american dollars. how many american dollars and how many british pound coins do you have?

The first thing we must do for this case is to define variables.
 We have then:
 x = british pound
 y = dollar bills
 We have the following system of equations:
 x + y = 17
 1.65x + y = 18.30
 Resolving we have:
 x = 2
 y = 15
 
 you have:
 american dollars = 15 items
 british pound coins = 2 items

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