## Choosing a Summer Job

### Dan SchmidtSanta Rosa District Schools

#### Description

Given two summer job opportunities, the student must determine when each job will earn the same amount and what that amount will be. This will be done by solving systems of equations.

#### Objectives

Using a rectangular coordinate system (graph), applies and algebraically verifies properties of two-and three- dimensional figures, including distance, midpoint, slope, parallelism, and perpendicularity.

Uses systems of equations and inequalities to solve real world problems graphically, algebraically, and with matrices.

Interprets data that has been collected, organized, and displayed in charts, tables, plots.

-Straight edge
-Worksheets
-Calculators

#### Preparations

1. Run off worksheets (make some extras).
2. Gather a straight edge for each student.

#### Procedures

Pre-requisite: Students must have prior knowledge of graphing linear equations and solving systems of equations by graphing, substitution and elimination.

1.Give situation of each job (on attached worksheet). Make a table with time (weekly through 8th week) as the independent variable and total amount of money as the dependent variable.

2. On the graph from the worksheet, label the y-axis in increments of 100 dollars. Then plot data points taken from the table in step one, ( Week (w), Total Amount (t)), and connect the data points for each individual job. Label each line as job 1 or job 2.

3. From the graph or data in the table, determine the slope and the y-intercept of each job situation. Place this information in standard form for linear equations ( Ax
+ By = C).

4. Determine when (time) the amount earned for both jobs will be the same and what that amount will be by solving a system of equations graphically, by substitution, and by elimination .

5. Solving systems of equations graphically: Find intersection of two lines from the graph.

6. Solving system of equations by substitution:
A) Take one equation and isolate either variable, (w) or (t);
B) Substitute isolated variable into second equation and solve.

7. Solving system of equations by elimination:
A) Ensure variables and equal sign are aligned in columns;
B) Eliminate one of the variables by using multiplication to make them opposites.

8. State which job will earn the most over an eight week period and what that amount will be.

#### Extensions

This lesson can very easily be manipulated by changing each job situation.

#### Attached Files

Worksheet and rubric.     File Extension: pdf