Math question!!!!! homework

ms. nguyen needs to separate $385 into three parts to pay some debts. the second part must be five times as large as the first part. the third part must be $35 more than the first part. how much money must be in each part?????????

Let:
A = first part
B = second part = 5A; the second part must be five times as large as the first part
C = third part = A + 35; the third part must be $35 more than the first part

Equations:
A + B + C = 385

Solution:
A + 5A + (A + 35) = 385
A + 5A + A + 35 = 385
A + 5A + A = 385 - 35
7A = 350
A = 50

B = 5A = (50) = 250

C = A + 35 = 50 + 35 = 85

Check:
A + B + C = 385
50 + 250 + 85 = 385
385 = 385 Yes!

Answer:
First part: $50
Second part: $250
Third part: $85

Total:385
1st part: x
2nd part: 5x
3rd part: x+35

x+5x+x+35=385
7x=385-35
7x=350
x=50

1st part: $50
2nd part: $250
3rd part: $85

a+b+c=385
5a=b
c=35+a
a+5a+35+a=385
7a=350
a=50
b=250
c=85