The population of a town increased by 16 2/3 % in 1990 and 10% in 1991. if the population of the town at the beginning of 1990 was 30,000, what was it at the end of 1991?

First, find the population at the end of 1990
At the end of 1990, the increase would be 16 2/3 % of 30,000, or we could write it as
i = % × 30,000

We need to change percent into proper fraction
i = % × 30,000
i = % × 30,000
percent means per hundred
i = × 30,000
i = × 30,000
i = 5,000

At the end of 1990, the population would be
p = 30,000 + 5,000
p = 35,000

Second, find the population at the end of 1991
The increase of the population would be 10% of 35,000, or we could write it as
i = 10% × 35,000
i = 0.1 × 35,000
i = 3,500

The population at the end of 1991 would be
p = 35,000 + 3,500
p = 38,500
This is the final answer

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