Let "x" = # of coins for quarters "y" = # of coins for nickels

then, x + y = 80 coins, right? This will be equation 1.

Next, when we multiply 0.25(quarter) by "x" (# of coins) +

nickel (.05) multiply by "y" (# of coins) equals $14.60 isn't it?

Equating that fact,

0.25x+0.05y=$14.60 and this is equation 2.

Going back to equation 1, we get "x = $80-y" . Then substitue this value to x in equation 2,

0.25($80-y)+0.05y=$14.60

$20-0.25y+0.05y=$14.60

$20-$14.60=0.20y

y=27 coins (nickels)

For x = 80-y= 80-27

   x= 53 coins (quarters)