# Cups

We have three cups. In the cups we had fluid and boredom we started to shed.

1 We shed one-third of the fluid from the second glass into the first and third.
2 Then we shed one quarter cup of liquid from the first to the second and to the third.
3 Then we shed one-fifth of the liquid from the third to the first cup and to the second.

Finally remained 8, 10 and 7 dl fluids in cups. How many dl of liquid was in the cups originally?

Correct result:

a =  6.5 dl
b =  14.5 dl
c =  4 dl

#### Solution:

d=a+b/3
e=b/3
f = c+b/3
k = d/2
l = e+d/4
m = f+d/4
x = k+m/5
y = l+m/5
z = m •3/5
x=8
y=10
z = 7

3a+b-3d = 0
b-3e = 0
b+3c-3f = 0
d-2k = 0
d+4e-4l = 0
d+4f-4m = 0
5k+m-5x = 0
5l+m-5y = 0
3m-5z = 0
x = 8
y = 10
z = 7

a = 13/2 = 6.5
b = 29/2 = 14.5
c = 4
d = 34/3 ≈ 11.333333
e = 29/6 ≈ 4.833333
f = 53/6 ≈ 8.833333
k = 17/3 ≈ 5.666667
l = 23/3 ≈ 7.666667
m = 35/3 ≈ 11.666667
x = 8
y = 10

Our linear equations calculator calculates it.

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