The jones family attends for $47.00 with two adults and three kids. the switch family attends when some friends are in town $74.75 with three adults and five kids. how much does the ramirez family have to pay with four adult sons and four kids ?

Set up a system of equations.
that means: 
2a+3k=47
3a+5k=74.75

Which means

6a+9k=141
6a+10k=149.5
If we subtract we get that 
-1k=-8.5
One kid costs 8.5 
Plug this back into the equation and you get that 25.5+2a=47. That means adults cost 10.75

Kids: 8.5 
Adults: 10.75

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