Liz harold has a jar in her office that contains 47 coins. Some are pennies and the rest are dimes.

Liz harold has a jar in her office that contains 47 coins. Some are pennies and the rest are dimes. If the total value of the coins is 2.18, how many of each denomination does she have?

Set up two equations where p is the number of pennies and d is the number of dimes:
(1) d + p = 47
(2) 0.1d + 0.01p = 2.18

Rearrange (1) into (3) by solving for d
(3) d = 47 - p

Substitute (3) into (2)
0.1(47 - p) + 0.01p = 2.18
4.7 - 0.1p + 0.01p = 2.18

Group p terms
4.7 - 0.09p = 2.18

Add 0.09p to both sides
0.09p + 2.18 = 4.7

Subtract 2.18 from both sides
0.09p = 2.52

Divide each side by 0.09
p = 28

Now substitute that back into (3)
d =47 - 28
d = 19