Answer:
[tex]14[/tex]
Step-by-step explanation:
We can set up the following system of equations:
[tex]\begin{cases}10d+5n=150\\d+n=22\\\end{cases}[/tex], where [tex]d[/tex] is the number of dimes she has and [tex]n[/tex] is the number of nickels she has.
Multiplying the second equation by -5 and adding both equations lets us isolate and solve for [tex]d[/tex]:
[tex]10d+5n+(-5(d+n))=150+(-5(22)),\\5d=40,\\d=8[/tex]
Plugging [tex]d=8[/tex] into any of the two equations will let us solve for [tex]n[/tex]:
[tex]8+n=22,\\n=\fbox{$14$}[/tex].
Therefore, she has 14 nickels.
