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.

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) (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."
Let this be equation 1.
"A second customer buys five MP3 players and four sets of headphones, and pays $785."
Let this be equation 2.
Now you have 2 equations and 2 variables.

Take equation 2 and solve for M:

Subtract 4H from both sides.

Divide both sides by 5 to get M alone.
Simplify.
Plug this M into equation 1 from above and solve for H.
Equation 1.

Distribute the 4.

Subtract 628 from both sides.

Multiply by 5.
Simplify.

Divide by 14.
So a set of headphones is $40.
Plug this back in the first equation:

So an MP3 player costs $125.
Check by plugging into the second equation.

It checks.

Answer by checkley77(12844) (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

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