the gasoline gauge on a van initially read 1/4 full. When 10 gallons were added to the tank the gauge read2/3 full. How many more gallons are needed to fill the tank?

Question

the gasoline gauge on a van initially read 1/4 full.  When 10 gallons were added to the tank the gauge read2/3 full.  How many more gallons are needed to fill the tank?

anonymous · Answer

1/4 + 2/3 = 3/12 + 8/12 = 11/12
Leaving 1/12 left to fill the tank.
I think....not 100% sure

anonymous · Answer

am I way off mathstudent ?

mathstudent55 · Answer

This is a little tricky.

anonymous · Answer

1/4 + 2/3 + 1/12 = 3/12 + 8/12 + 1/12 = 12/12 (full tank)

mathstudent55 · Answer

Adding 10 gallons of gas is not adding 2/3 of the tank to teh 1/4 tank that was already there.

anonymous · Answer

yes this is very confusing to me!

mathstudent55 · Answer

Adding 10 gallons made the tank 2/3 full.

anonymous · Answer

10 gallons fills 5/12 up. Does that make sense. 2/3 - 1/4 = 8/12 - 3/12 = 5/12

mathstudent55 · Answer

OK, think of it like this.
The full tank takes x gallons.

mathstudent55 · Answer

The tank was reading 1/4 full. That means the tank has (1/4)x gallons, 
or 0.25x gallons.

mathstudent55 · Answer

Then 10 gallons were added. That means
0.25x + 10

mathstudent55 · Answer

After adding the 10 gallons, the tank reads 2/3 full. This is (2/3)x, so
0.25x + 10 = (2/3)x

anonymous · Answer

10 gallons is 5/12, so 20 gallons is 10/12 ...right ?

mathstudent55 · Answer

yes

mathstudent55 · Answer

(1/4)x + 10 = (2/3)x
Multiply both sides by 12 to get rid of parentheses:
3x + 120 = 8x

mathstudent55 · Answer

subtract 3x from both sides
120 = 5x

mathstudent55 · Answer

Divide both sides by 5:
x = 24

mathstudent55 · Answer

The fill tanks has a 24-gallon capacity.

anonymous · Answer

you are so smart.....I am jealous :)

mathstudent55 · Answer

Since the tanks became 2/3 full by adding the 10 gallons, it still needs 1/3 of its capacity to be full.
1/3 of 24 gallons = 8 gallons

mathstudent55 · Answer

Now le's check 24 gallons to see if it's correct.

anonymous · Answer

1/4(24) + 10 = 2/3(24)
8 + 10 = 16 ....are you sure

mathstudent55 · Answer

The tank was 1/4 full.
1/4 of 24 gal is 6 gal.
Then 10 gal was added. Now the tanks has 6 gal + 10 gal = 16 gal
This is 2/3 of the tank. 16/24 = 2/3, so it's correct.
The answer is 8 gallons.

mathstudent55 · Answer

1/4 0f 24 = 6
1/3 of 24 = 8

anonymous · Answer

oops...I did it wrong...it does equal

mathstudent55 · Answer

We use both 1/4 tank in the beginning of the problem, and 1/3 tank at the end.

anonymous · Answer

you should be a teacher

mathstudent55 · Answer

thanks