SOLUTION: Translate the following into a system of equations, then solve it. A customer walks into an electronics store and buys four MP3 players and six sets of headphones, paying $740.

Algebra ->  Linear-equations -> SOLUTION: Translate the following into a system of equations, then solve it. A customer walks into an electronics store and buys four MP3 players and six sets of headphones, paying $740.       Log On


   

Question 184977: Translate the following into a system of equations, then solve it.
A customer walks into an electronics store and buys four MP3 players and six sets of headphones, paying $740. A second customer buys five MP3 players and four sets of headphones, and pays $785. How much does an MP3 player cost? How much does a set of headphones cost?
Found 2 solutions by SandyBeach, checkley77:
Answer by SandyBeach(2) About Me  (Show Source):
You can put this solution on YOUR website!
Let M be a MP3 player, and let H be a headphone.
"A customer walks into an electronics store and buys four MP3 players and six sets of headphones, paying $740."
4M+%2B+6H+=+740 Let this be equation 1.
"A second customer buys five MP3 players and four sets of headphones, and pays $785."
5M+%2B+4H+=+785 Let this be equation 2.
Now you have 2 equations and 2 variables.
4M+%2B+6H+=+740
5M+%2B+4H+=+785
Take equation 2 and solve for M:
5M+%2B+4H+=+785
5M+%2B+4H+-4H=+785-4H Subtract 4H from both sides.
5M+%2B+cross%284H%29+-cross%284H%29=+785-4H
5M=+785-4H
5M%2F5=+785%2F5-4H%2F5 Divide both sides by 5 to get M alone.
M=+highlight%28157-4H%2F5%29 Simplify.
Plug this M into equation 1 from above and solve for H.
4M+%2B+6H+=+740 Equation 1.
4%2Ahighlight%28%28157-4H%2F5%29%29+%2B+6H+=+740
highlight%284%29%2A157-highlight%284%29%2A4H%2F5+%2B+6H+=+740 Distribute the 4.
628-16H%2F5+%2B+6H+=+740
628-highlight%28628%29-16H%2F5+%2B+6H+=+740-highlight%28628%29 Subtract 628 from both sides.
-16H%2F5+%2B+6H+=+112
-16H%2A5%2F5+%2B+6%2A5H+=+112%2A5 Multiply by 5.
-16H+%2B+30H+=+560 Simplify.
14H+=+560
14H%2F14+=+560%2F14 Divide by 14.
H+=+40 So a set of headphones is $40.
Plug this back in the first equation:
4M+%2B+6H+=+740
4M+%2B+6%2840%29+=+740
4M+%2B+240+=+740
4M+%2B+240+-+240+=+740+-+240
4M+=+500
4M%2F4+=+500%2F4
M+=+125
So an MP3 player costs $125.
Check by plugging into the second equation.
5M+%2B+4H+=+785
5%28125%29+%2B+4%2840%29+=+785
625+%2B+160+=+785
785+=+785 It checks.

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
4m+6h=740 multiply by 5
5m+4h=785 multiply by -4
20m+30h=3,700
-20m-16h=-3,140
-------------------------
14h=560
h=560/14
h=$40 is the cost of headphones.
4m+6*40=740
4m+240=740
4m=740-240
4m=500
m=500/4
m=$125 is the price of the MP3 unit.
Proof:
5*125+4*40=785
625+160=785
785=785