Question 979813
A family has a coin jar that is now full. The children count the change and calculate the total value to be $44.08. 

Let Q represent the number of quarters and use 
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Let's also let each coin be represented by the 1st letter in the spelling of
the coin:
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The children count the change and calculate the total value to be $44.08,
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that's the same as 4408 cents.

25Q + 10D + 5N + P = 4408 
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There are:
151 more dimes than quarters
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D = Q + 151
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8 times as many nickels as quarters
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N = 8Q
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15 more than 18 times as many pennies as quarters
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P = 18Q + 15

25Q + 10D + 5N + P = 4408
D = Q + 151
N = 8Q
P = 18Q + 15

In the first equation substitute for D, N, and P

25Q +     10D     +  5N   +     P    = 4408
 |         |          |         |    |   |
25Q + 10(Q + 151) + 5(8Q) + 18Q + 15 = 4408

Solve that equation for Q, then find D, N, and P by substituting 
what you get for Q in these three equations:

D = Q + 151
N = 8Q
P = 18Q + 15

I won't tell you the answers but there are 1034 coins total.  So
when you get your answers add them up and see if you get 1034.

Edwin</pre>