#### Answer

$27$ nickels
$53$ quarters

#### Work Step by Step

Nickel = 5 cents = 0.05 dollars.
Quarters = 25 cents = 0.25 dollars.
Let $n$ be the number of nickels.
Let $q$ be the number of quarters.
A jar containing 80 coins, all of which are either quarters or nickels:
$n+q=80$.
The total value of the coins is $14.60$:
$0.05n+0.25q=14.60$.
$n+q=80$
$0.05n+0.25q=14.60$
$q=80-n$
$0.05n+0.25(80-n)=14.60$
$0.05n+20-0.25n=14.60$
$-0.20n+20=14.60$
$-0.20n=-5.40$
$0.20n=5.40$
$n=27$
$n+q=80$
$q=80-n$
$q=80-(27)$
$q=53$
$27$ nickels
$53$ quarters