Question

41 coins, consisting of nickels and quarters, have a total value of $4.65. How many nickels and pennies are there?

Answer 1

You will need to start with something very easy.

`x` = cents for pennies

`y` = cents for quarters

After that, we make a longer equation.

`x+y=41`

Now, we have the basics.

`5x+25y=465 (cents)`

Moving onto a harder equation:

`y=41-x`

We took the
`x+y=41`, '
`x`' and put it after the 41, but the
`y` stays the same.

We put this equation into the '
`5x+25y=465`' and cancel out both
`y`s

Now, we have an easier equation:

`5x+25(41-x)=465\\\\25*41+(5x-25x)=465\\\\25*41+(-20x)=465\\`

We cannot solve the
`x` like this so, we bring the
`25*41` to the right side.

`-20x=465-(25*41)\\\\-20x=465-1025\\\\\\-20x=-560\\\\20x=560\\\\x=28`

We can now solve for
`y`.

`28+y=41\\\\\\41-28=y\\\\y=13`

13 quarters and 28 pennies. Hope this helped!