Question

There is a shop selling new compact disks and used compact disks. John bought 3 new compact disks and 8 used compact disks for $133.89. Michel bought 6 new compact disks and 2 used compact disks for $127.92. Find the cost of buying one used compact disk

Answer 1

The price of a used compact disk is $9.99.

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,

What is the system of equations?

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

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.

To learn more about the equation visit:

brainly.com/question/2972832

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