Question 210631
Let C=total cost of lessons



So at first, the cost is $50. So no matter how long she stays, she'll be paying $50. So at first, the cost is {{{C=50}}}



Now let's say that she now decides to do another month on top of the first month. She's already paid $50, but she now has to pay an extra $30. So for one additional month, the cost is now {{{C=50+30=80}}}. If she does it for another month after that, she has to pay another $30, giving the cost of {{{C=50+30+30=50+60=110}}}



Now let's say that she does 8 additional months. This means that she has to pay 8 $30 fees. So the cost would be {{{C=50+30+30+30+30+30+30+30+30=290}}} (there are 8 thirty's here)


To save time and sanity, instead of adding repeated values, we can just multiply. So instead of having eight 30's out there, we can rewrite that part as {{{8*30}}}. 


So in general, if she stays for 'x' additional months, you're going to add on 'x' charges of $30 which will cost {{{30x}}}. Add this to the original cost of $50 to get the total charge {{{C=30x+50}}}



Since we want to hold the cost to $350 (that's her budget), we simply make {{{C=350}}} and plug it in to get {{{350=30x+50}}}



Note: you can rearrange the last equation to get {{{30x+50=350}}}