Question 321015
Let {{{m}}} = months belonging to either club

Let {{{C[a]}}} = total cost to belong to A
Let {{{C[b]}}} = total cost to belong to B
Given:
{{{C[a] = 28m + 15}}}
{{{C[b] = 24m + 16}}}
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When will {{{C[a] = C[b]}}}?
{{{28m +  15 = 24m + 16}}} 
{{{4m = 1}}}
{{{m = 1/4}}}
The memberships will be the same after 1/4 month, or 1 week
check:
{{{C[a] = 28m + 15}}}
{{{C[a] = 28*(1/4) + 15}}}
{{{C[a] = 7 + 15}}}
{{{C[a] = 22}}}
{{{C[b] = 24m + 16}}}
{{{C[b] = 24*(1/4) + 16}}}
{{{C[b] = 6 + 16}}}
{{{C[b] = 22}}}
OK