<PRE><B>Question 89046</B>

        Translate the following into a system of equations, then solve it: 
A customer walks into an electronics store and buys five MP3 players and eight sets of headphones, paying $840. A second customer buys three MP3 players and four sets of headphones, and pays $480. How much does an MP3 player cost? How much does a set of headphones cost? 

    Let the cost of 1 MP3 player be = $ X

       cost of 5 MP3 players will be = $5X
    Let the cost of 1 headphone  be = $ y
       cost of 8 sets of headphones = $ 8Y

    Total cost of 5MP3 and 8 headphones = $840
                           i.e, 5X+8Y = 840..........eq&#39;n(1)

     cost of 3MP3                   = $ 3X
     cost of 4 sets of headphones  =  $4Y
   
    Total cost of 3MP3   and 4 headphones = $480
                            i.e, 3X+4Y = 480..........eq&#39;n(2)


    solving eq&#39;n(1) &amp;eq&#39;n(2)    multiply eq&#39;n(2) by 2  we get 6X+8Y = 960...(3)
                subtract (1) from (3)   we get X = 120

     substitute for x in 3X+4Y = 480

                         3(120)+4Y = 480
                                 4y = 480-360 = 120  or Y = 120/4 = 30

        Therefore the cost of 1 MP3  player = $ 120
              
                   the cost of 1 headphone = $ 30

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