Once you have your first equation, go to your answer choices to determine which answers you can
eliminate. You’ll quickly see that (A), (C), and (D) are all wrong, so you can select (B) without even
having to construct the second equation.
Now try one on your own!
7.To save on helium costs, a balloon is inflated with both helium and nitrogen gas. Between
the two gases, the balloon can be inflated up to 8 liters in volume. The density of helium is
0.20 grams per liter, and the density of nitrogen is 1.30 grams per liter. The balloon must
be filled so that the volumetric average density of the balloon is lower than that of air,
which has a density of 1.20 grams per liter. Which of the following system of inequalities
best describes how the balloon will be filled, if x represents the number of liters of helium
and y represents the number of liters of nitrogen?A)
B)
C)
D)
Here’s How to Crack It
Start with the most straightforward piece of information and translate that. In this case, it is probably the
information about the total volume of the balloon. “Between the two gases” would indicate addition, and
the gases are represented as x and y, so you need x + y in the correct answer. They all have that, so go to
the next piece. Together, x and y can be “up to 8 liters.” This translates to “less than or equal to 8,”
because the balloon’s volume can’t be greater than 8, but it could be 8 or less. Therefore, one equation
must be x + y ≤ 8. You can eliminate (A) and (B), as those answers have different equations related to x +
y. The next part may be hard to translate, so pick some numbers and try them out. Make x = 2 and y = 2.
The second equation in (D) is easier to work with, so see if these numbers make that equation true. 0.2(2)
- 1.30(2) = 0.4 + 2.60 = 3. This is not less than 1.20, so eliminate (D) and choose (C).