Juan has 15 coins, all nickels and dimes. this collection of coins is worth $0.90. how many nickels and dimes are there?

Call the nickels = n
Call the dimes = d

Equations.
n + d = 15                   (1)

0.05n + 0.10d = 0.90  Multiply through by 100 
5n + 10d = 90             Divide by 5 
n + 2d = 18                 (2)

Solve
Begin by subtracting (1) from (2)
n + 2d = 18
n + d   = 15                   the ns cancel out.
       d =    3

Now put this result into equation (1)
n + d = 15
n + 3 = 15 Subtract 3 from both sides.
n = 15 - 3
n = 12

Check
5n + 10d = 90
5*12 + 3*10 = ?90
60 + 30 = 90 and it does check

Note the trick with this problem is to get rid of the decimals.
It makes it much easier to work with whole numbers.

Neither is the answer