You will need to start with something very easy.
[tex]x[/tex] = cents for pennies
[tex]y[/tex] = cents for quarters
After that, we make a longer equation.
[tex]x+y=41[/tex]
Now, we have the basics.
[tex]5x+25y=465 (cents)[/tex]
Moving onto a harder equation:
[tex]y=41-x[/tex]
We took the [tex]x+y=41[/tex], '[tex]x[/tex]' and put it after the 41, but the [tex]y[/tex] stays the same.
We put this equation into the '[tex]5x+25y=465[/tex]' and cancel out both [tex]y[/tex]s
Now, we have an easier equation:
[tex]5x+25(41-x)=465\\\\25*41+(5x-25x)=465\\\\25*41+(-20x)=465\\[/tex]
We cannot solve the [tex]x[/tex] like this so, we bring the [tex]25*41[/tex] to the right side.
[tex]-20x=465-(25*41)\\\\-20x=465-1025\\\\\\-20x=-560\\\\20x=560\\\\x=28[/tex]
We can now solve for [tex]y[/tex].
[tex]28+y=41\\\\\\41-28=y\\\\y=13[/tex]
13 quarters and 28 pennies. Hope this helped!
