Let R be the original number of red    marbles; 
    B be the original number of blue   marbles; 
    G be the original number of green  marbles; 
    P be the original number of purple marbles.


For these quantities, we have this equation

    R + B + G + P = 1153.    (1)


After changes,

    - the number of red   marbles is 2R;

    - the number of blue  marbles is 0.5B;

    - the number of green  marbles is G-30;

    - the number of purple marbles is P+20.


We also are given that 

    2R = 0.5B = G-30 = P+20 = k,

where k is the common value of marbles of each of four colors after changes.


Thus  R = 0.5k;  B = 2k;  G = k+30;  P = k-20.


We substitute these expressions into equation (1). 
We then get this equation for single unknown k

    0.5k + 2k + (k+30) + (k-20) = 1153.


Simplify and find k

    4.5k = 1153 - 30 + 20

    4.5k = 1143

       k = 1143/4.5 =  254.


So, the number of red    marbles originally was 0.5*254 = 127;

    the number of blue   marbles originally was 2*254 = 508;

    the number of green  marbles originally was 254+30 = 284;

    the number of purple marbles originally was 254-20 = 234.

Let x = the common number of each color Sally had at the end.

At the beginning she had: 
half as many reds, or 0.5x reds.
twice as many blues, or 2x blues.
30 more greens, or x+30 greens.
20 fewer purples, or x-20 purples.

So





At the beginning she had: 
0.5x = 0.5(254) = 127 reds.
2x = 2(254) = 508 blues.
x+30 = 254+30 = 284 greens.
x-20 = 254-20 = 234 purples.

Edwin