Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis; Jay Abramson; Sharon North; Amy Baldwin; Alyssa Howell

Activity

Use this information to answer questions 1 - 2.

To help pay for his tuition, a college student plans to work in the evenings and on weekends. He has been offered two part-time jobs: working in the guest-services department at a hotel and waiting tables at a popular restaurant.

The job at the hotel pays $18 an hour and offers $33 in transportation allowance per month.

The job at the restaurant pays $7.50 an hour plus tips. The entire wait staff typically collects about $50 in tips each hour. Tips are divided equally among the 4 wait staff members who share a shift.

The equation $7.50 h + \frac{50}{4} h = 18 h + 33$ represents a possible constraint about a situation for 1 month.

1.

Solve the equation and check your solution.

Compare your answer: $h = 16.5$

$7.50 h + \frac{50}{4} h = 18 h + 33$

$7.50 (16.5) + \frac{50}{4} (16.5) = 18 (16.5) + 33$

$123.75 + 206.25 = 297 + 33$

$330 = 330 ✓$

2.

Add a scale on the number line so that the point marked with a circle represents the solution to the equation you found in question 1.

A blank number line is shown with an open circle on a point in the middle.

Compare your answer:

Your answer may vary, but here is a sample.

3.

Which job pays better if he works fewer hours than the solution you found in question 1?

Hotel Job.

4.

Explain how you know.

Compare your answer:

Your answer may vary, but here is a sample. The hotel job pays better if he works fewer than 16.5 hours a month because I found the pay for both jobs using numbers that are less than 16.5 and found that pay at the hotel job is always higher.

5.

Which job pays better if he works more hours than the solution you found in question 1?

Restaurant Job.

6.

Explain how you know.

Compare your answer:

Your answer may vary, but here is a sample. The restaurant job pays better if he works more than 16.5 hours a month because I found the pay for both jobs using numbers that are more than 16.5 and found that pay at the restaurant job is always higher.

7.

Draw a number line, including a scale, so that the point marked with a circle represents the solution to the inequality: $7.50 h + \frac{50}{4} h < 18 h + 33$ .

Compare your answer:

Your answer may vary, but here is a sample.

8.

Draw a number line, including a scale, so that the point marked with a circle represents the solution to the inequality: $7.50 h + \frac{50}{4} h > 18 h + 33$ .

Compare your answer:

Your answer may vary, but here is a sample.

9.

Explain how you know.

Compare your answer:

Your answer may vary, but here are some samples.

Inequality 1 shows the pay at the hotel $(18 h + 33)$ being greater than the pay at the restaurant $7.50 h + \frac{50}{4}$ . Earlier, we found out that the hotel job is better when the student works less than 16.5 hours. Graph B shows $h < 16.5$ . This means Graph B shows the solution to Inequality 1.
If we substitute a value greater than 16.5 for $h$ , we have a true statement for Inequality 2 and a false statement for Inequality 1. This means $h > 16.5$ is a solution to Inequality 2 but not to Inequality 1.
If we substitute a value less than 16.5 for $h$ , we have a true statement for Inequality 1 but not for Inequality 2. So $h < 16.5$ is a solution to Inequality 1.

2.9.4 Making Sense of Inequalities and Their Solutions

Activity