Question

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

Answer 1

You first have to make an simple equation.

`x` = How many pennies

`y` = How many quarters

After that, since a penny is 5 Cents and a quarter is 25 Cents, we make the equation as:

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

To write the whole entire thing in an equation is:

`x + y = 41`

`y = 41 - x` Since I brought the x from the left to right, we change the positive "
`x`" to negative "
`y`"

To bring the '
`y = 41 - x`' to
`5x + 25y = 465`, we get rid of the "
`y`"s from both equations.

Now, you are left with the simplified equation:

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

`25*41+5x-20x=465`

`-20x+25*41=465`

`-20x=465-(25*41)`

`-20x=465-1025`

`-20x=-560`

`20x=560`

`x=28`

Now you find the
`y`.

`x` = 28

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

Conclude:

So the y was the quarter and the x was the pennies.

Quarters = 13

Pennies = 28