Put  the total number of pennies Mollie has is:a

We have\(\left\{{}\begin{matrix}a-3⋮5\\a-1⋮7\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}a-8⋮5\\a-8⋮7\end{matrix}\right.\)\(\Rightarrow a-8\in BC\left(5,7\right)=\left\{0,35,70,105,.......\right\}\)

\(\Rightarrow a\in\left\{8,43,78,113,.........\right\}\)

Because a\(⋮\)3 and a<100 so a=78

So the total number of pennies Mollie has is 78 pennies

Let \(\overline{ab}\) be the number of pennies Mollie has. 

Since \(\overline{ab}\) is divided by 5 with remainder 3, b = 3 ; 8

If b = 3, \(\overline{a3}⋮3\) and a = 0 ; 3 ; 6 ; 9

If b = 8, \(\overline{a8}⋮3\) and a = 1 ; 4 ; 7

Only 78 is divided by 7 with remainder 1. So, Mollie has 78 pennies