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?

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) (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) (Show Source): You can put this solution on YOUR website!
c=cds d=dvds

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

.

.

.

now subtract the 2 equations

divide by 20

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

subtract 48.06

if rounded up it would be $7.44 per dvd
check with second equation

hmm guess i shouldnt of rounded up
.

subtract 48.03

.

ok that works
so dvds are $7.4425 each and cds are $8.005 each
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