Let w = number of 1 cent coins, x = number of 5 cent coins, y = number of 10 cent coins, and z = number of 25 cent coins.

We know two things.

\(0.01w+0.05x+0.1y+0.25z=175\)

\(w+x+y+z=3576\)

Let's eliminate w because we can.

\(0.01(3576-x-y-z)+0.05x+0.1y+0.25z=175\)

\(0.04x+0.09y+0.24z=139.24\)

There will be more than one solution for this problem. Let's settle for finding just one of them by saying z=0 and y=0.

\(0.04x=139.24\)

\(x=3481\)

\(w+3481=3576\)

\(w=95\)

One solution to this problem would be 95 one cent coins, 3481 five cent coins 0 ten cent coins, 0 twenty-five cent coins.