394 algebra De mystif ieD
- Px Qx
Rxx
=+ =−
=+ −30 2405
30 2405
()()- PxQx
Rxx
=− =+
=− +150005 250 10
150005 250 10..
(. .)()- Px Qx
Rxx
=+ =−
=+ −40 2801
() 40 28 () 0For the problems in this section, we will be given some specific revenue and
are asked to find the price that brings in this revenue. Because we found the
revenue equations earlier, all we need to do here is to solve the quadratic equa-
tion. Some of these problems have two solutions.EXAMPLES
A department store sells 20 music players per week at $80 each. The man-
ager believes that for each decrease of $5 in the price, six more players will
be sold.
Let x represent the number of $5 decreases in the price.P = 80 – 5x Q = 20 + 6x R = (80 – 5x)(20 + 6x).What price should the manager charge if the revenue needs to be $2240?R = (80 – 5x)(20 + 6x) becomes 2240 = (80 – 5x)(20 + 6x)
2240 = (80 – 5x)(20 + 6x)
2240 = 1600 + 380x – 30x^2
30 x^2 – 380x + 640 = 0
1
1030 380 640 1
10( xx^2 – + ) = () 0
3 x^2 – 38x + 64 = 0
(3x – 32)(x – 2) = 0
3 x – 32 = 0 x – 2 = 0
3 x = 32 x = 2
x = ^32
3
If x = ^32
3, the price for each player is P = 80 – 532 = $.
3 26 67
.EXAMPLES
A department store sells 20 music players per week at $80 each. The man-
ager believes that for each decrease of $5 in the price, six more players willEXAMPLES
A department store sells 20 music players per week at $80 each. The man-