For solving systems of inequalities, at my workplace I often teach combining them by adding them together. In fact, you'd be surprised how many of these types of questions appear to specifically be
designed to be solve this way. Let's try that here.
First, write the inequalities so that the inequality sign faces the same direction. Doing so here we get:
r + s + t > 1
0 > s + t
Now let's add them together. So we'll add everything on the left side together, then everything on the right side together. Doing so we get:
r + s + t > 1 + s + t
Now let's simplify. Both sides have an "s+t", so let's subtract s+t from both sides. And watch what we'll get!
r + s + t - s - t > 1 + s + t - s - t
See how the "s" and "t" will cancel out from both sides now? So we'll end up with:
r > 1
And what do you know?!? That's exactly what we're looking for. Coincidence? Not at all! So the answer will be B, Quantity B is greater.
So keep in mind...for systems of inequalities, always look to see if you can add the inequalities together. There's a high probability that you'll
coincidentally end up with the EXACT thing you're looking for in the question!
_________________
Corey
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