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

Answer: 3 pennies