When 200 gallons of oil were removed from a tank, the volume of oil

D
(1) 1/2*x-3/7*x=200 , can solve for x
(2) x-1600=3/7*x

Let the total volume of the tank be X. Therefore X-200 = 3/7(x). I derived this information from the question stem. Where am i going wrong in my approach??

This is not correct because we don't know whether the tank initially was full to capacity. So, it should be x - 200 = 3/7*t, where x is the initial volume of the liquid and t is the total capacity of the tank.

When 200 Gallons was removed - 3/7 was left of tank's capacity.

With this in order to calculate the tanks capacity, we need to know what does 200 gallons corresponds to or what is the remaining 3/7 capacity corresponds to.

(1) Before the 200 gallons were removed, the volume of oil in the tank was \(\frac{1}{2}\) of the tank's capacity.

Provides information on what 200 gallons corresponds to overall tank volume, hence sufficient.

(2) After the 200 gallons were removed, the volume of the oil left in the tank was 1,600 gallons less than the tank's capacity.

Provides information on what the 3/7th volume corresponds to, hence sufficient.

Answer is D

Each of the Statement is sufficient.

For st1 -
We know that half capacity will be 3.5/7T, so earlier volume was 3.5/7 and now 3/7T
Difference before and after removing 200 gallons: 3.5/7T-3/7T = 0.5T/7
So we can derive 0.5/7T = 200

Getting this from other forum and credit to the author.

we cannot use one variable to represent both the starting volume and the capacity of the tank, because it is never stated that the tank starts out full.

We have to create another variable for the capacity: t, and keep it separate from the starting volume: x.

x - 200 = (3/7)t, "what is t?"

The above is a single linear equation in two variables, so the introduction of any independent linear equation that relates the variables x and t will allow us to solve.

Statement 1) this statement says that the starting volume (x) was 1/2 of the capacity (t), so x = (1/2)t. Immediately we can see that this is an independent linear equation that will allow us to solve for t, so it is sufficient.

Just to illustrate the calculation, [(1/2)t] - 200 = (3/7)t, so t = 200 * 14 = 2,800 gallons.

Statement 2) this statement says that the volume after 200 is removed is 1,600 gallons less, so x - 200 = t - 1,600.

Since x - 200 = (3/7)t, as given in the question stem, we can substitute to get [(3/7)t] = t - 1,600. Again, this statement is sufficient because it introduces a new linear equation that relates t and x.

The calculation (unnecessary at this point) is (4/7)t = 1,600, so t = 2,800 gallons.

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