Answer:
Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.
Step-by-step explanation:
Let 10-oz, 14-oz, and 20-oz coffees be represented by the variables <em>a, b</em>, and <em>c</em>, respectively.
Since a total of 14 cups of coffee was served:

A total of 204 ounces of coffee was served. Therefore:

A total of $16.70 was collected. Hence:

This yields a triple system of equations. In order to solve a triple system, we should isolate the system to only two variables first.
From the first equation, let's subtract <em>a</em> and <em>b</em> from both sides:

Substitute this into both the second and third equations:

And:

In this way, we've successfully created a system of two equations, which can be more easily solved. Distribute:
For the Second Equation:

And for the Third:

We can solve this using substitution. From the second equation, isolate <em>a: </em>
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Substitute into the third:

Distribute and simplify:

Therefore:

Using the equation for <em>a: </em>
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And using the equation for <em>c: </em>
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Therefore, Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.