SOLUTION: At Al's Rent-a-Center, it costs $30 more per month to rent a leather couch than it does to rent a microfiber couch. Pauline rented a leather couch for 8 months and then exchanged i

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: At Al's Rent-a-Center, it costs $30 more per month to rent a leather couch than it does to rent a microfiber couch. Pauline rented a leather couch for 8 months and then exchanged i      Log On


   



Question 561152: At Al's Rent-a-Center, it costs $30 more per month to rent a leather couch than it does to rent a microfiber couch. Pauline rented a leather couch for 8 months and then exchanged it for a microfiber couch, which she rented for 12 months. She paid a total of $1620 to rent these couches. Solve this system of equations to find the monthly rental charge for each couch.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = charge / month for microfiber couch
Let +b+ = charge / month for leather couch
given:
(1) ++b+=+a+%2B+30+
(2) +12a+%2B+8b+=+1620+
---------------------
Substitute (1) into 2)
(2) +12a+%2B+8%2A%28+a+%2B+30+%29+=+1620+
(2) +12a+%2B+8a+%2B+240+=+1620+
(2) +20a+=+1620+-+240+
(2) +20a+=+1380+
(2) +a+=+69+
and
(1) ++b+=+a+%2B+30+
(1) +b+=+69+%2B+30+
(1) +b+=+99+
$69 / month for microfiber couch
$99 / month for leather couch
check:
(2) +12%2A69+%2B+8%2A99+=+1620+
(2) +828+%2B+792+=+1620+
(2) +1620+=+1620+
OK