Question

Need help with this math​

Answer 1

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:

$\frac{1}{3}+10gallons=\frac{3}{4}$    (1)

$10gallons=\frac{3}{4}-\frac{1}{3}$   (2)

$1gallon=\frac{1}{24}$    (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:

$\frac{3}{4}+X=1$   (4)

$X=\frac{1}{4}$   (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 $1gallon=\frac{1}{24}$ . So, we can write the following relation to transform from fractions of a tank to gallons:

$\frac{1}{4}.\frac{1gallon}{\frac{1}{24}}=(\frac{1gallon}{4})(\frac{24}{1})$

$\frac{24}{4}gallons=6gallons$

Therefore:

6 more gallons are needed to fill the tank