One cent coin: two cent coin = (1/6): (1/5) = 5: 6 =15:18.

One cent coin: five cent coin = (1/4): (1/3) = 3: 4 =15: 20.

So the thickness ratio

A penny: two cents: five cents = 15: 18: 20

When they are stacked into a cylinder with the same height, the number ratio of coins is:

Penny: Penny: Penny = (115): (118): (1/20) =12.

So in 124 coins,

There are124×12/(12+10+9) = 48 coins.

There are124×10/(12+10+9) = 40 binary coins.

There are124× 9/(12+10+9) = 36 nickels.

Total face value = 0.01× 48+0.02× 40+0.05× 36 = 3.08 yuan.

==================

Solve by equation:

Let 1 min, 2-cent and 5-cent coins have X, Y and Z respectively, and their heights are h 1, h2 and H3 respectively;

According to the problem, h2=5h 1/6, h3=3h 1/4, Xh 1=Yh2=Zh3.

Y=5X/6，Z=3X/4。

Because X+Y+Z= 124.

X+5X/6+3X/4= 124。

X=48，Y=5/6*48=40，Z=3/4*48=36。

Total face value = 48 *1+40 * 2+36 * 5 = 308 = 3.08 yuan.

I hope it helps you.