Question 1204074
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D:E = 2:1
D/E = 2/1
D/E = 2
D = 2E


C:D = 4:5
C/D = 4/5
5C = 4D  ...... cross multiply
5C = 4(2E) .... plug in D = 2E
5C = 8E
C = 8E/5


B:C = 3:1
B/C = 3/1
B/C = 3
B = 3C
B = 3*(8E/5) ...... plug in C = 8E/5
B = 24E/5


A:B = 2:3
A/B = 2/3
3A = 2B  ...... cross multiply
A = (2/3)*B
A = (2/3)*(24E/5) ...... plug in B = 24E/5
A = 16E/5


Each block of steps shown above has us isolate variables A, B, C, and D such that E is the only variable on the right hand side.
A = 16E/5
B = 24E/5
C = 8E/5
D = 2E


This will allow us to do substitutions in the next set of steps to let us solve for E.


A+B+C+D+E = 18900
16E/5+24E/5+8E/5+2E+E = 18900
5*(16E/5+24E/5+8E/5+2E+E) = 5*18900
16E+24E+8E+10E+5E = 94500
63E = 94500
E = 94500/63
<font color=red>E = 1500</font>


Use this to find the other variables
A = 16E/5 = 16*1500/5 = 4800
B = 24E/5 = 24*1500/5 = 7200
C = 8E/5 = 8*1500/5 = 2400
D = 2E = 2*1500 = 3000


To summarize
A = 4800
B = 7200
C = 2400
D = 3000
<font color=red>E = 1500</font>


I'll let the student verify each of those values. 
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