SOLUTION: I've been trying to solve this word problem and I can't. I've spend so much time on it. I was wondering If you could give me a hand, this is the problem; mary has 1.76 in change

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Question 834630: I've been trying to solve this word problem and I can't. I've spend so much time on it. I was wondering If you could give me a hand, this is the problem;
mary has 1.76 in change. She has four less dimes than pennies, but one more dime then twice the number of quarters. She also has one more nickel then quarters. How many of each kind of coins does May have.
thank you
Ricky

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let,
1.D=P-4
2.D=1%2B2Q
3.N=Q%2B1
0.01P%2B0.05N%2B0.10D%2B0.25Q=1.76
4.P%2B5N%2B10D%2B25Q=176
From eq. 1,
P=D%2B4
From eq. 2,
2Q=D-1
Q=%281%2F2%29%28D-1%29=D%2F2-1%2F2
from eq. 3,
N=Q%2B1=D%2F2-1%2F2%2B1=D%2F2%2B1%2F2
Now substitute all of those into eq. 4 and solve for D.
%28D%2B4%29%2B5%28D%2F2%2B1%2F2%29%2B10D%2B25%28D%2F2-1%2F2%29=176
Multiply by 2 to get rid of fractions,
2%28D%2B4%29%2B5%28D%2B1%29%2B20D%2B25%28D-1%29=352
2D%2B8%2B5D%2B5%2B20D%2B25D-25=352
52D=352%2B25-5-8
52D=364
D=7
Then back substituting,
P=D%2B4=7%2B4=11
N=D%2F2%2B1%2F2=7%2F2%2B1%2F2=8%2F2=4
Q=D%2F2-1%2F2=7%2F2-1%2F2=6%2F2=3