To join a gym, you pay a one-time fee of $75 and $45 per month for the duration of the membership. You have paid a total of $345. How long have you been a member of the gym?

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Answer 1 · 2016-10-22T03:12:53

You have been a member for 6 months.

Let #x=# the number of months you've been a member.

The total variable cost is #x# multiplied by the monthly fee of $45.
The fixed cost is $75.
The total cost is then #45x+75#, which equals $345#.

Then the equation will be

#45x +75=345#

#color(white)(aaa)-75color(white)(a)-75color(white)(aaa)#Subtract 75 from both sides

#color(white)(aa)45xcolor(white)(a)=color(white)(a)270#

#color(white)(aa)(45x)/45color(white)a=color(white)a270/45color(white)(aaa)#Divide both sides by 45

#color(white)(aaa)xcolor(white)a=color(white)a6# months