SOLUTION: Hi the total mass of A, B C D was 280kg. If the mass of A decreased by 30kg, the mass of B was increased by 10kg, the mass of C was halved and the mass of D was tripled, the 4 mas

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Question 1120748: Hi
the total mass of A, B C D was 280kg. If the mass of A decreased by 30kg, the mass of B was increased by 10kg, the mass of C was halved and the mass of D was tripled, the 4 masses would be equal. Find the mass of each.
Thanks
Found 2 solutions by Shin123, ankor@dixie-net.com:
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
a%2Bb%2Bc%2Bd=280
a=b%2B40
a-40=b
c=2b%2B20
d=c%2F6 Substitute b+40 for a,
b%2B40%2Bb%2Bc%2Bd=280
2b%2B40%2Bc%2Bd=280 Substitute 2b+20 for c,
2b%2B40%2B2b%2B20%2Bd=280
4b%2B60%2Bd=280 Substitute (2b+20)/6 for d,
4b%2B60%2B%281%2F3%29b%2B%2810%2F3%29=280
%2813%2F3%29b%2B%28190%2F3%29=280
%2813%2F3%29b%2B%28190%2F3%29=840%2F3
%2813%2F3%29b=650%2F3
highlight%28b=50%29
a-40=50
highlight%28a=90%29
c=2%2850%29%2B20
highlight%28c=120%29
d=120%2F6
highlight%28d=20%29 So the masses are a=90,b=50,c=120,and d=20. Check:90+50=140+120=260+20=280.90-30=60. 50+10=60. 120/2=60. 20*3=60. Correct.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
the total mass of A, B C D was 280kg.
a + b + c + d = 280
If the mass of A decreased by 30kg, the mass of B was increased by 10kg,
the mass of C was halved and the mass of D was tripled, the 4 masses would be equal
a - 30 = 3d
a = (3d+30)
:
b + 10 = 3d
b = (3d-10)
:
.5c = 3d
c = 6d
Replace a, b, c in the first equation
(3d+30) + (3d-10) + 6d + d = 280
combine like terms
13d + 20 = 280
13d = 280 - 20
13d = 260
d = 260/13
d = 20 kg
then
a = 3(20) + 30
a = 90 kg
and
b = 3(20) - 10
b = 50 kg
and
c = 6(20)
c = 120 kg
:
Check: 90 + 50 + 120 + 20 = 280
: