5pls writing world sells pens with a company's logo printed on the pens. writing world charges a standard price per box of pens when the customer purchases 200 or fewer boxes. each box over 200 that the customer purchases is sold at a discounted rate.a customer purchases x boxes of pens,where x≥200 . the average cost of a single box of pens purchased by this customer is represented by 1600+6(x−200)x .what is the meaning of the parts of this rational expression in the context of the situation? select from the drop-down menus to correctly complete each statement.the numerator of the rational expression represents either price paid per box or total amount paid or amount paid for pens over 200. the standard price for the first 200 boxes of pens is either $6 or $8 or $24. when the customer orders 500 pens, the amount spent on pens offered at the discounted rate is either $1200 or $1600 or $1800.

Correct answer is:- standard price for first 200 boxes is 8$ and the amount spent on the pens offered at discounted rate is 1800$.

Solution:-

We are given that for first 200 pens, there is a standard price. Let the standard price be y.

So if some one purchases pens fewer than 200 then amount to pay =200y.

If  number of boxes is more than 200, then each box over 200 is given at a discounted rate. Let the discounted rate be d.

Then price of the x boxes if x>200 is (standard price * 200)+( x-200)*d

                                                          = 200y+(x-200)d

Hence price of each box =

If we compare above equation with given equation,

200y=1600 and (x-200)d=6(x-200)

 y=8 and d=6.

a)Hence standard price for first 200 boxes=8$

And discounted price per box which is over 200 boxes=6$

b)If the customers order 500 boxes of pens then the amount spent on pens offered at discounted rate = (number of boxes over 200)*(discounted rate)

                               =(500-200)*6=1800$

Line BL belongs to triangle BCL
Line CM belons to triangle BCM

The triangles BCL and BCM has a coomon side, the side BC, this side is congruent. 

If Angle XBA = Angle YCA, then:
Angle ABC or angle MBC of triangle BCM = Angle ACB or angle LCB of triangle BCL

If line BE is the bisector of angle ABC, then divides it into two equal parts, then angle MBL must be congruent with angle LBC

If line CD is the bisector of angle ACB, then divides it into two equal parts, then angle LCM must be congruent with angle MCB

As angle MBC is congruent with angle LCB, the angles MBL, LBC, LCM, and MCB must be congruents too.

Then angle MCB in triangle MBC is congruent with angle LBC of triangle BCL.

Then, the two triangles BCM and BCL have a congruent side (BC) and the two adjacent angles are congruent too (angle MBC of triangle BCM with angle  LCB of triangle BCL, and angle MCB of triangle BCM with angle LBC of triangle BCL).
Then by ASA the two triangles are congruents and the other two sides must be congruents too: Line BL of triangle BCL must be congruent with line CM of triangle BCM (because they are opposite to congruent angles: BL in triangle BCL is opposite to angle LCB, and CM in triangle BCM is opposite to angle MBC, and angles LCB and MBC are congruents).

I would use ASA to help me prove Line BL= Line CM