Robert is a high school basketball player. In a particular game, he made some three point shots and some free throws (worth one
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<u>Part a)</u> Use a system of inequalities to model the scenario
Let
x-------> represent babysitting hours
y-------> represent tutoring hours
we know that
--------> inequality
--------> inequality
<u>Part b)</u> Use the model created in part A to create a graph representing Jeanne’s probable income earned and possible number of hours worked this week
we know that
--------> inequality
This inequality represent Jeanne’s possible number of hours worked this week
Using a graph tool
the solution of this inequality is the shaded area
see the attached figure N
--------> inequality
This inequality represent Jeanne’s probable income earned this week
Using a graph tool
the solution of this inequality is the shaded area
see the attached figure N
<u>Part c)</u> Analyze the set of coordinate values that represent solutions for the model created in part A. Choose one of the coordinates within the solution and algebraically prove that the coordinate represents a true solution for the model
we have the system of inequalities
--------> inequality
--------> inequality
the solution of the system of inequalities is the shaded area
using a graph tool
see the attached figure N
Let
------> see the attached figure N
The point belongs to the shaded area, so it is a system solution.
If the point is a solution, it must satisfy both inequalities.
<u>Prove algebraically </u>
substitute the value of x and y in the inequalities
<u>inequality </u>
------> is ok
<u>inequality </u>
-------> is ok
the point A satisfy both inequalities
therefore
the point A is a solution of the system
Since Joann receives $10 per hour for the first 35 hours, so she receives $350 (35 times $10) before she starts receiving extra hours.
Since she received $515, we know that she worked extra hours.
Let's use the variable x to represent the number of extra hours worked.
So we can write the following equation for the total payment received:
She worked 11 extra hours. Adding this to the 35 regular hours, so she worked for 46 hours.