SOLUTION: please help The cost of six CDs and four DVDs is $77.80; and the cost of fourteen DVDs and eleven CDs is $192.25. How much do a CD and a DVD cost?

Algebra ->  Equations -> SOLUTION: please help The cost of six CDs and four DVDs is $77.80; and the cost of fourteen DVDs and eleven CDs is $192.25. How much do a CD and a DVD cost?      Log On


   

Question 615961: please help
The cost of six CDs and four DVDs is $77.80; and the cost of fourteen DVDs and eleven CDs is $192.25. How much do a CD and a DVD cost?
Found 2 solutions by Theo, JBarnum:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
c = number of cd's that were bought.
d = the number of dvds that were bought.
6c + 4d = 77.80
11c + 14d = 192.25
use one of the equations to solve for d in terms of c.
then use that value for d in the other equation.
from the first equation, you get:
6c + 4d = 77.80
subtract 6c from both sides of the equation to get:
4d = 77.80 - 6c
divide both sides of the equation by 4 to get:
d = (77.80 - 6c) / 4
substitute this equation for d in the other equation to get:
11c + 14d = 192.25 becomes:
11c + 14*((77.80-6c)/4) = 192.25
simplify by removing parentheses to get:
11c + (1089.2 - 84c)/4 = 192.25
multiply both sides of the equation by 4 to get:
44c + 1089.2 - 84c = 769
subtract 1089.2 from both sides of the equation to get:
44c - 84c = 769 - 1089.2
simplify to get:
-40c = -320.2
divide both sides of the equation by -40 to get:
c = 8.005
take the first original equation and replace c with 8.005 and solve for d.
the first original equation is:
6c + 4d = 77.80
replace c with 8.005 to get:
6*8.005 + 4d = 77.80
simplify to get:
48.03 + 4d = 77.80
subtract 48.03 from both sides of the equation to get:
4d = 77.80 - 48.03
simplify to get:
4d = 29.77
divide both sides of the equation by 4 to get:
d = 7.4425
you have:
c = 8.005
d = 7.4425
substitute these values for c and d in the second original equation.
11c + 14d = 192.25 becomes:
11*8.005 + 14*74425 = 192.25
simplify to get:
88.055 + 104.195 = 192.25 which becomes:
192.25 = 192.25 confirming the values for c and d are correct.

Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
c=cds d=dvds
6c%2B4d=77.8
11c%2B14d=192.25
personally i think elimination method with eliminating the dvds would be the easiest. 14 gos into 28 2 times and 4 goes into 28 7 times
so multiply the top equation by 7 and bottom equation bt 2
7%286c%2B4d%29=7%2877.8%29
2%2811c%2B14d%29=2%28192.25%29
.
7%286c%2B4d%29=7%2877.8%29
42c%2B28d=544.6
.
2%2811c%2B14d%29=2%28192.25%29
22c%2B28d=384.5
.
42c%2B28d=544.6%29
22c%2B28d=384.5%29 now subtract the 2 equations
42c-22c=20c
28d-28d=0
544.6-384.5=160.1
20c%2B0=160.1divide by 20
c=8.005
if rounding up then its $8.01 per cd
now take that number and put it in for c in one of the original equations
6c%2B4d=77.8
6%288.01%29%2B4d=77.8
48.06%2B4d=77.8 subtract 48.06
4d=29.74
d=7.435
if rounded up it would be $7.44 per dvd
check with second equation
11c%2B14d=192.25
11%288.01%29%2B14%287.44%29=192.25
88.11%2B104.16=192.27hmm guess i shouldnt of rounded up
.
6%288.005%29%2B4d=77.8
48.03%2B4d=77.8 subtract 48.03
4d=29.77
d=7.4425
.
11c%2B14d=192.25
11%288.005%29%2B14%287.4425%29=192.25
88.055%2B104.195=192.25 ok that works
so dvds are $7.4425 each and cds are $8.005 each