1. ## Finding the capacity

Two oil tanks,X and Y, have the same capacity. The amount of oil in tank X is 1/2 of its capacity, and the amount of oil in tank Y is 1200 gallons less than its capacity. If there are 7800 gallons of oil in the two tanks combined, what is the capacity, in gallons, of tank X?

How is it 6000?

2. ## Re: Finding the capacity

Originally Posted by donnagirl
Two oil tanks,X and Y, have the same capacity. The amount of oil in tank X is 1/2 of its capacity, and the amount of oil in tank Y is 1200 gallons less than its capacity. If there are 7800 gallons of oil in the two tanks combined, what is the capacity, in gallons, of tank X? How is it 6000?
Can you solve $\frac{C}{2}+C-1200=7800~?$

3. ## Re: Finding the capacity

I set it up this way:
C1 is the capacity of X.
C2 is the capacity of Y.
0.5*C1 = C2 - 1200
C1 + C2 = 7800
But when I substitute I get a positive 1200 instead of negative.

C1 + 0.5C1 + 1200 = 7800

4. ## Re: Finding the capacity

Originally Posted by donnagirl
I set it up this way:
C1 is the capacity of X.
C2 is the capacity of Y.
0.5*C1 = C2 - 1200
C1 + C2 = 7800
But when I substitute I get a positive 1200 instead of negative.
C1 + 0.5C1 + 1200 = 7800
That setup is simply wrong.
If you solve $\frac{C}{2}+C-1200=7800~?$, you will get $C=6000$.

5. ## Re: Finding the capacity

How can I deduce the right setup (to show where your equation comes from).

6. ## Re: Finding the capacity

Hello, donnagirl!

Two oil tanks, X and Y, have the same capacity.
The amount of oil in tank X is 1/2 of its capacity,
and the amount of oil in tank Y is 1200 gallons less than its capacity.
If there are 7800 gallons of oil in the two tanks combined,
what is the capacity, in gallons, of tank X?

How is it 6000?

$\text{The two tanks have the }same\;capacity.$
. . $\text{Hence: }\:C \,=\,\text{the capacity of tank }X\,=\,\text{the capacity of tank }Y.$

$\text{The amount of oil in tank }X\text{ is: }\:\tfrac{1}{2}C$

$\text{The amount of oil in tank }Y\text{ is: }\:C - 1200$

$\text{So we have: }\:\tfrac{1}{2}C + (C - 1200) \:=\:7800$

$\text{Got it?}$

7. ## Re: Finding the capacity

Originally Posted by Soroban
Hello, donnagirl!

$\text{The two tanks have the }same\;capacity.$
. . $\text{Hence: }\:C \,=\,\text{the capacity of tank }X\,=\,\text{the capacity of tank }Y.$

$\text{The amount of oil in tank }X\text{ is: }\:\tfrac{1}{2}C$

$\text{The amount of oil in tank }Y\text{ is: }\:C - 1200$

$\text{So we have: }\:\tfrac{1}{2}C + (C - 1200) \:=\:7800$

$\text{Got it?}$

How is that different from reply #2?

8. ## Re: Finding the capacity

He didn't say it was different; he simply explained HOW (which you didn't do).

9. ## Re: Finding the capacity

Can somebody kick this Thompson guy outta here? Keeps doing this to post his link!
Tired of getting emails due to his posts...