What are the volumes of the three bottles in gallons and in liters?

Question

This is from Page 198, #16 of Fundamentals of Technical Mathematics (2nd edition): Stacey wants to determine the volume in liters of three oddly shaped bottles. All has is a 1-gal (3.8 L) container filled with water. After much experimenting she finds the following. The gallon exactly fills all three containers. Twice the volume of the second container exactly fills the first and third. Three times the volume of the third exactly fills the first. What are the volumes of the three bottles in gallons and in liters?

Correction: it's actually #15

Answer 1

1 Gallon= 1st + 2nd + 3rd.
2(2nd)=1st+3rd.
3(3rd)=1st

Now the hard part.
Plugin in 3(3rd) for 1st. ( get third equation to second equation.
2(2nd)=3(3rd)+3rd
2(2nd)=4(3rd)
2nd=2(3rd)
Plug these into the first equation.
1L=2(3rd)+3rd+3(3rd)
1L=6(3rd)
so then you get.
the 3rd is 1/6L
the 1st=3(3rd)=3(1/6)=1/2
the 2nd is 1/3 since 1-1/6-1/2=1/3
Good luck.