We can write the formula for how much a member pays as:
#m = $14 + $4c#
Where:
#m# is the total cost for a member
#c# is the number of aerobic classes a member attends
We can write the formula for how much a non-member pays as:
#n = $6c#
Where:
#m# is the total cost for a non-member
#c# is the number of aerobic classes a non-member attends
What we are trying to find is when #m = n# so we can write and solve this for #c# (the number of aerobic classes) as:
#$14 + $4c = $6c#
First, we will subtract #color(red)($4c)# from each side of the equation to isolate the #c# term while keeping the equation balanced:
#$14 + $4c - color(red)($4c) = $6c - color(red)($4c)#
#$14 + 0 = ($6 - $4)c#
#$14 = $2c#
Now we divide each side of the equation by #color(red)($2)# to solve for #c# while keeping the equation balanced:
#($14)/color(red)($2) = ($2c)/color(red)($2)#
#(color(red)(cancel(color(black)($)))14)/color(red)(cancel($)2) = (color(red)(cancel(color(black)($)))color(red)(cancel(color(black)(2)))c)/color(red)(cancel($)cancel(2))#
#7 = c#
#c = 7#
