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.