Aclothing store office very often various promotions to attract customers but wants to maintain the same amount of profit to do this the store mark up prices above retail and then advertises a deal that results in a markdown equivalent to a retail price the retail prices of a necktie is $59.99 the store offers a buy 2 get 1 free deal on neckties what is the new retail price during this promotion what is the markup and what is the markup percent on a tie during the promotion.

Since 3 neckties will be out from the store, so you need to know how much is the cost of 3 ties.

$59.99 x 3 = $179.97 and divide it by two because the costumer will only pay for 2

$179.97 / 2 = $89.99 is the new price

Mark up = 89.99 – 59.99 = $30.00

% mark up = [(89.99/59.99) -1] * 100

= 50%

 

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