Respuesta :

Answer: 6 gallons

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:

6 more gallons are needed to fill the tank