Keith has p pennies, n nickels, and d dimes in his pocket. the total number of coins is 9. the expression 0.01p+0.05n+0.10d0.01p+0.05n+0.10d represents the value of the coins, which is equal to $0.53. he has two fewer nickels than dimes. how many pennies does keith have?

The total number of coins is 9. Therefore  
  p+n+d = 9                (1)
There are two fewer nickels than dimes. Therefore
  n = d - 2                  (2)
From (1) and (2), obtain
p+(d-2)+d = 9
p + 2d = 11                
p = 11 - 2d                                           (3)
Total value:
0.01p + 0.05n + 0.10d = 0.53             (4)
Substitute (2) and (3) into (4).
0.01(11-2d) + 0.05(d-2) + 0.10d = 0.53
0.11 - 0.02d + 0.05d - 0.10 + 0.10d = 0.53
0.03d + 0.01 = 0.53
0.13d = 0.52
d = 4
p = 11 - 2d = 11 - 8 = 3
3 pennies