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!