Question

Janis was offered two different jobs when she graduated from college. She made the graph and table to show how much she would earn over time at each job.

Earnings over Time for Job 1
Earnings over Time for Job 2

A graph entitled Earnings over Time for Job 1 has year on the x-axis and earnings in dollars on the y-axis. A line with positive slope goes through (0, 40,000) and (10, 60,000). y = 2,000 x + 40,000.

A 2-column table entitled Earnings over time for job 2 has 7 rows. The first column is labeled year with entries 10, 12, 14, 16, 18, 20, 22. The second column is labeled Earnings in dollars with entries 55,000, 60,000, 65,000, 70,000, 75,000, 80,000, 85,000.

When will Janis’s salary be the same for job 1 and job 2, and how much will she be earning at that point?
The salaries will be the same in year 20, and she will be earning $80,000.
The salaries will be the same in year 16, and she will be earning $70,000.
The salaries will be the same in year 12, and she will be earning $60,000.
The salaries will be the same in year 10, and she will be earning $55,000.

Answer 1

Year 20; she will be earning $80,000.

Work: Job 1: y = 2000x + 40,000. Job 2 is linear through (10,55,000) and (12,60,000) so y = 2500x + 30,000.
Set equal: 2000x + 40,000 = 2500x + 30,000 → 10,000 = 500x → x = 20. Then y = 2000(20)+40,000 = $80,000.