Question 184977
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 + 6H = 740}}}  Let this be equation 1.

"A second customer buys five MP3 players and four sets of headphones, and pays $785."

{{{5M + 4H = 785}}}  Let this be equation 2.

Now you have 2 equations and 2 variables.

{{{4M + 6H = 740}}}  
{{{5M + 4H = 785}}}

Take equation 2 and solve for M:
{{{5M + 4H = 785}}}
{{{5M + 4H -4H= 785-4H}}}  Subtract 4H from both sides.
{{{5M + cross(4H) -cross(4H)= 785-4H}}}  
{{{5M= 785-4H}}}  
{{{5M/5= 785/5-4H/5}}}  Divide both sides by 5 to get M alone.
{{{M= highlight(157-4H/5)}}}  Simplify.

Plug this M into equation 1 from above and solve for H.

{{{4M + 6H = 740}}} Equation 1.
{{{4*highlight((157-4H/5)) + 6H = 740}}}  
{{{highlight(4)*157-highlight(4)*4H/5 + 6H = 740}}} Distribute the 4.
{{{628-16H/5 + 6H = 740}}} 
{{{628-highlight(628)-16H/5 + 6H = 740-highlight(628)}}} Subtract 628 from both sides.
{{{-16H/5 + 6H = 112}}} 
{{{-16H*5/5 + 6*5H = 112*5}}} Multiply by 5.
{{{-16H + 30H = 560}}} Simplify.
{{{14H = 560}}} 
{{{14H/14 = 560/14}}} Divide by 14.
{{{H = 40}}} So a set of headphones is $40.

Plug this back in the first equation:
{{{4M + 6H = 740}}} 
{{{4M + 6(40) = 740}}}  
{{{4M + 240 = 740}}}  
{{{4M + 240 - 240 = 740 - 240}}} 
{{{4M = 500}}} 
{{{4M/4 = 500/4}}}  
{{{M = 125}}} 

So an MP3 player costs $125. 

Check by plugging into the second equation.
{{{5M + 4H = 785}}}  
{{{5(125) + 4(40) = 785}}}  
{{{625 + 160 = 785}}}  
{{{785 = 785}}}  It checks.