system of equations

Question

Hanz and Mario went to a sale at a music store where all the CD's were one price and all cassettes were another price. Hanz bought 2 CD's and 2 cassettes for $40.00, while Mario bought 1 CD and 4 cassettes for $44.00.

 

The equations below represent these purchases, where x is the cost of a CD and y is the cost of a cassette. 

 

Hanz: 2x+2y=40       Mario: x+4y=44  

 

What are the costs of a single CD and a single cassette? Solve the system of equations by either constructing a graph on a sheet of graph paper or by using an algebraic process. Explain how you determined the costs. Use words, symbols,or both in your explanation

Answer 1

y=8 ; x=12 so one Cd costs $12 and one cassette costs $8.

 

You must first find the value for y which is 20-x, plug that in for the second equation and solve for x by isolating the x variable. You will find that x equals 12 and y equals 8.

 

I hope that this helps. Contact me for personalized tutoring services.

Answer 2

If x+4y=44, then x=44-4y.

Substituting in the other equation, we have

 

2(44-4y)+2y=40

88-8y+2y=40

-6y=-48

y=8

 

Then, substituting in x+4y=44, we have

 

x+4(8)=44

x=12

 

So, CDs cost $12 each and cassettes cost $8 each.