You first have to make an simple equation.
[tex]x[/tex] = How many pennies
[tex]y[/tex] = How many quarters
After that, since a penny is 5 Cents and a quarter is 25 Cents, we make the equation as:
[tex]5x + 25y = 465[/tex] (cents)
To write the whole entire thing in an equation is:
[tex]x + y = 41[/tex]
[tex]y = 41 - x[/tex] Since I brought the x from the left to right, we change the positive "[tex]x[/tex]" to negative "[tex]y[/tex]"
To bring the '[tex]y = 41 - x[/tex]' to [tex]5x + 25y = 465[/tex], we get rid of the "[tex]y[/tex]"s from both equations.
Now, you are left with the simplified equation:
[tex]5x+25(41-x)=465\\[/tex]
[tex]25*41+5x-20x=465[/tex]
[tex]-20x+25*41=465[/tex]
[tex]-20x=465-(25*41)[/tex]
[tex]-20x=465-1025[/tex]
[tex]-20x=-560[/tex]
[tex]20x=560[/tex]
[tex]x=28[/tex]
Now you find the [tex]y[/tex].
[tex]x[/tex] = 28
[tex]28+y=41\\41-28=y\\y=13[/tex]
Conclude:
So the y was the quarter and the x was the pennies.
Quarters = 13
Pennies = 28
