If the project is finished within 26 weeks of its start, the project manager will receive a bonus of $1,000; and if the project
is finished within 27 weeks of its start, the bonus will be $500. Find the probability of each bonus. (Round Mean, Standard Deviation, z-value to 2 decimal places and Probability to 4 decimal places.) Path Mean Std. Dev. a-d-e-h 24.33 1.35 a-f-g 15.50 1.26 b-i-j-k 14.83 1.02 c-m-n-o 26.17 1.66 Probability ($1,000) .4099 Probability ($500)
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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.