Question

In a pile of 55 coins made of nickels and dimes totaling $3.90 how many of each coin are there

Answer 1

There are 5 pennies in a nickel, and 10 pennies in a dime.  Now in $3.90 there are 390 pennies.

n = number of nickels in the pile

d = number of dimes in the pile

we know the pile has 55 coins, therefore whatever "n" and "d" are, we know that n + d = 55.

now, "n" is how many nickel coins are there, how many pennies is it in total?  well, 5 pennies to a nickel, for "n" nickels, will then be 5(n) or 5n.

and "d" is how many dime coins are there, so therefore in "d" coins, there are 10(d) pennies, or 10d.

we also know the total amount of pennies is 390, therefore 5n + 10d = 390.

$\bf \begin{cases} n+d=55\implies \boxed{n}=55-d\\ 5n+10d=390\\ -------------\\ 5\left(\boxed{55-d} \right)+10d=390 \end{cases} \\\\\\ 275-5d+10d=390\implies 5d=115\implies d=\cfrac{115}{5}\implies d=23$

how many nickel coins are there anyway?  well, n = 55 - d.