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:

`(1)/(3)+10gallons=(3)/(4)` (1)

`10gallons=(3)/(4)-(1)/(3)` (2)

`1gallon=(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:

`(3)/(4)+X=1` (4)

`X=(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=(1)/(24)` . So, we can write the following relation to transform from fractions of a tank to gallons:

`(1)/(4).(1gallon)/((1)/(24))=((1gallon)/(4))((24)/(1))`

`(24)/(4)gallons=6gallons`

Therefore:

6 more gallons are needed to fill the tank