SOLUTION: Lakota bought 6 new compact disks and 2 used compact disks for $127.92. At the same prices, Mackenzie bought 3 new compact disks and 8 used compact disks for $133.89. Find the cost

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Lakota bought 6 new compact disks and 2 used compact disks for $127.92. At the same prices, Mackenzie bought 3 new compact disks and 8 used compact disks for $133.89. Find the cost      Log On


   

Question 210725: Lakota bought 6 new compact disks and 2 used compact disks for $127.92. At the same prices, Mackenzie bought 3 new compact disks and 8 used compact disks for $133.89. Find the cost of buying a single used compact disk.
Answer by algebrapro18(249) About Me  (Show Source):
You can put this solution on YOUR website!
Well this is a system of 2 equations and 2 unknowns. Let n = the price of new compact disks and let u = the price of used compact disks. Then the first equation would be 6n + 2u = 127.92. The second equation would be 3n+8u = 133.89.

So our system is

6n + 2u = 127.92
3n+8u = 133.89

Since I don't like working with decimals I would multiply both equations by 100 that way it would get rid of the decimal. Doing so results in the following system:

600n+200u = 12792
300n+800u = 13389

now we want to know how much one used disk sells for. to do that we multiply the bottom equation by -2 and add it to the top equation.

-2(300n+800u = 13389) => -300n-1600u = -26778

Now we add that to the top equation

600n+200u = 12792
+(-300n-1600u = -26778)
----------------------------
-1400u = -13987


now we solve for u by dividing both sides by -1400 and we see that u = 9.99.

So the price of a used compact disk is $9.99.