need help with this math
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First we are told that we initially had 1/3 of the tank and when 10 gallons were added we had 3/4 of the tank:
[tex]\frac{1}{3}+10gallons=\frac{3}{4}[/tex] (1)
[tex]10gallons=\frac{3}{4}-\frac{1}{3}[/tex] (2)
[tex]1gallon=\frac{1}{24}[/tex] (3)
This means 1 gallon is equivalent to 1/24 tank.
On the other hand if we have 3/4 of a tank and need to reach 1 tank we have to add another fraction of the tank:
[tex]\frac{3}{4}+X=1[/tex] (4)
[tex]X=\frac{1}{4}[/tex] (5)>>>>This is the fraction needed to complete 1 tank
Now we need to know how much that 1/4 tank is equivalent in gallons.
From (3) we know [tex]1gallon=\frac{1}{24}[/tex] . So, we can write the following relation to transform from fractions of a tank to gallons:
[tex]\frac{1}{4}.\frac{1gallon}{\frac{1}{24}}=(\frac{1gallon}{4})(\frac{24}{1})[/tex]
[tex]\frac{24}{4}gallons=6gallons[/tex]
Therefore: