need the answer please!!

Question

olivia has 81 coins consisting of pennies, dimes, and quarters, and they are worth $14.25. If the number of quarters is twice the sum of the other two coins, then how many of each type does she have?

Answer 1

P be the number of pennies
D be the number of dimes
Q be the number of quarters
P + D + Q = 81 eq. 1
Q = 2(P +D) eq. 2
.01P + .1D + .25Q = 14.25 eq. 3
subsitute eq. 2 to eq. 1
P + D + 2(P + D) = 81
P + D + 2P + 2D = 81
3P + 3D = 81 -----> P + D = 27
since P + Q + D + 81 and we know (P + D = 27) we substitute 27 into eq. 1 (27 + Q = 81) ----> Q = 54

 

fast forward a little bit ----------------------> -1.95 = -.09P  ------------> P ≈  21.666

P is supposed to be an integer. ?????? something wrong with problem. Maybe I missed something????