Let

'x' be the amount of money that angie made

'y' be the amount of money that marie made

'z' be the amount of money that gwen made

We need to find x, y, z.

All together they made x + y + z = 130

x = 20 + y (angie made 20$ more than marie)

z = y - 31 ( gwen made 31 less than marie)

We get the solution by solving the system of 3 linear equations:

x = 20 + y

z = y - 31

x + y + z = 130

or

20 + y + y + y - 31 = 141

3y = 141

y = 47$

x = 67$

z = 16$

ange made 67$, marie made 47$ and gwen made 16$