Call the number of dimes [tex]d[/tex] and the number of quarters [tex]q[/tex].
We know that:
[tex]d+q=29[/tex]
and
[tex]0.10d+0.25q=5.45[/tex]
By substitution:
[tex]d=29-q[/tex]
[tex]0.10(29-q)+0.25q=5.45[/tex]
[tex]2.9-0.10q+0.25q=5.45[/tex]
[tex]0.15q=2.55[/tex]
[tex]q=\frac{2.55}{0.15}[/tex]
[tex]q=17[/tex]
There are 17 quarters in the bank.
The question doesn't ask for it but we can also show that:
[tex]d=29-q[/tex]
[tex]d=29=17[/tex]
[tex]d=12[/tex]
There are 12 dimes in the bank.
