Question 703763
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 $1380/20=${{{highlight(69)}}} 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+$30=${{{highlight(99)}}}.
 
SYSTEM OF EQUATIONS:
{{{x}}} = monthly rental for the leather couch
{{{y}}} = monthly rental for the microfiber couch
{{{x=y+30}}} 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 ${{{8x}}}.
The charges for the 12 month rental of the microfiber couch were ${{{12y}}}.
The total rental charges, in $, were
{{{8x+12y=1620}}}
We have the system
{{{system(x=y+30,8x+12y=1620)}}} , which is tailor-made for substitution
{{{8(y+30)+12y=1620}}} --> {{{8y+8*30+12y=1620}}} --> {{{8y+240+12y=1620}}} --> {{{20y+240=1620}}} --> {{{20y=1620-240}}} --> {{{20y=1380}}} --> {{{y=1380/20}}} --> {{{highlight(y=69)}}}.
{{{system(x=y+30,y=69)}}} --> {{{x=69+30}}} --> {{{highlight(x=99)}}}.