SOLUTION: A company that manufactures hair ribbons knows that the number of ribbons it can sell each week, x, is related to the price p per ribbon by the equation x=1300−100p. At wha

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A company that manufactures hair ribbons knows that the number of ribbons it can sell each week, x, is related to the price p per ribbon by the equation x=1300−100p. At wha      Log On


   



Question 1054868: A company that manufactures hair ribbons knows that the number of ribbons it can sell each week, x, is related to the price p per ribbon by the equation
x=1300−100p. At what price should the company sell the ribbons if it wants the weekly revenue to be $4,200?
(Remember: The equation for revenue is R=xp.)

Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+R+=+4200+
+R+=+x%2Ap+
(1) +4200+=+x%2Ap+
(2) +x+=+1300+-+100p+
-----------------------------
(1) +p+=+4200%2Fx+
(2) +x+=+1300+-+100%2A%28+4200%2Fx+%29+
(2) +x%5E2+=+1300x+-+420000+
(2) +x%5E2+-+1300x+=+-420000++
Complete the square
(2) +x%5E2+-+1300x++=+-420000+
(2) +x%5E2+-+1300x+%2B+%28+1300%2F2+%29%5E2+=+-420000+%2B+%28+1300%2F2+%29%5E2+
(2) +x%5E2+-+1300x+%2B+650%5E2+=+-420000+%2B+650%5E2+
(2) +x%5E2+-+1300x+%2B+422500+=+-420000+%2B+422500+
(2) +%28+x+-+650+%29%5E2+=+2500+
(2) +%28+x+-+650+%29%5E2+=+50%5E2+
(2) +x+-+650+=+50+
(2) +x+=+700+
----------------------
and
(1) +4200+=+x%2Ap+
(1) +p+=+4200%2F700+
(1) +p+=+6+
The price/ribbon is $6
----------------------
check:
(2) +x+=+1300+-+100p+
(2) +700+=+1300+-+100%2A6+
(2) +700+=+1300+-+600+
(2) +700+=+700+
and
(1) +4200+=+x%2Ap+
(1) +4200+=+700%2A6+
(1) +4200+=+4200+
OK

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A company that manufactures hair ribbons knows that the number of ribbons it can sell each week, x, is related to the price p per ribbon by the equation
x=1300−100p. At what price should the company sell the ribbons if it wants the weekly revenue to be $4,200?
(Remember: The equation for revenue is R=xp.)
R = xp
4,200 = p(1,300 - 100p) ------- Substituting 4,200 for R and 1,300 - 100p for x
%224%2C200%22+=+%221%2C300%22p+-+100p%5E2
100p%5E2+-+%221%2C300%22p+%2B+%224%2C200%22+=+0
100%28p%5E2+-+13p+%2B+42%29+=+100%280%29 ------ Factoring out GCF, 100
p%5E2+-+13p+%2B+42+=+0
(p - 7)(p - 6) = 0
p, or price of each ribbon in order to realize revenue of $4,200: highlight_green%28matrix%281%2C3%2C+%22%247%22%2C+or%2C+%22%246%22%29%29