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

Question 703763: 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 the microfiber couch, which she rented for 12 months. She paid a total of $1620 to rent these couches. What is the monthly rental charge for each couch?
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I know how to do substitution, but my household has worked over and over in trying to come up with 2 equations that make sense.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
THE FIFTH GRADER SOLUTION:
Pauline should have saved $30 a month for the first 8 months (a total of $30x8=$240) by renting the microfiber couch all along.
Then she would have paid only $1620-$240=$1380 to have the microfiber couch for the whole 20 months (8 months + 12 months).
If you can rent a microfiber couch for 20 months for $1380, it costs $1380/20=$ per month to rent a microfiber couch.
A leather couch is more expensive and renting one for a month cost $30 more for a total of $69+$30=$.

SYSTEM OF EQUATIONS:
= monthly rental for the leather couch
= monthly rental for the microfiber couch
because it costs $30 more per month to rent a leather couch than it does to rent a microfiber couch.
The charges for the 8 month rental of the leather couch were $.
The charges for the 12 month rental of the microfiber couch were $.
The total rental charges, in $, were

We have the system
, which is tailor-made for substitution
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