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