SOLUTION: 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.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 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.       Log On


   

Question 163292: 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?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

1st customer:
5MP%2B8HP=840 ----------------------> eqn 1
In eqn 1 we get,
HP%2B%28840-5MP%29%2F8 -------------------> eqn 2
2nd customer:
3MP%2B4HP=480 ----------------------> eqn 3
Subst. eqn 2 in eqn 3:
3MP%2Bcross%284%291%28%28840-5MP%29%2Fcross%288%292%29=480
3MP%2B%28%28840-5MP%29%2F2%29=480, get LCD
%286MP%2B840-5MP%29%2F2=480, cross multiply
6MP-5MP=2%2A480-840=960-840=120
MP=120%2Fea, cost of a MP3
Via eqn 2:
HP=%28840-5%2A120%29%2F8=%28840-600%29%2F8=240%2F8
HP=30%2Fea, cost of Headphone set
In doubt? GO back eqn 3:
3%2A120%2B4%2A30=480
360%2B120=480
480=480
Go back eqn 1:
5%2A120%2B8%2A30=840
600%2B240=840
840=840
Thank you,
Jojo