18. PRACTICE Sandra was hired as a part-time office assistant. The amount of money she earns in a week is proportional to the number of hours she works during the week. She earned $167 for working 20 hours during her first week on the job. During the second week she worked 35 hours and earned $292.25. a. Identify the constant of proportionality in this situation. 167 =8.35 292.25 35 8.35 20 b. Sandra worked for 28 hours during the third week. How much money did she earn? $233.00 c. Create a graph showing how much Sandra will earn for working 5, 10, 15, 20, and 25 hours a week.
18. PRACTICE Sandra was hired as a part-time office assistant. The amount of money she earns in a week is proportional to the number of hours she works during the week. She earned $167 for working 20 hours during her first week on the job. During the second week she worked 35 hours and earned $292.25. a. Identify the constant of proportionality in this situation. 167 =8.35 292.25 35 8.35 20 b. Sandra worked for 28 hours during the third week. How much money did she earn? $233.00 c. Create a graph showing how much Sandra will earn for working 5, 10, 15, 20, and 25 hours a week.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Lesson 4: Direct Variation**
**Rate of Change**
**18. Practice Problem**
Sandra was hired as a part-time office assistant. The amount of money she earns in a week is proportional to the number of hours she works during the week. She earned $167 for working 20 hours during her first week on the job. During the second week, she worked 35 hours and earned $292.25.
**a. Identify the constant of proportionality in this situation.**
\[ \frac{167}{20} = 8.35 \]
\[ \frac{292.25}{35} \approx 8.35 \]
**b. Sandra worked for 28 hours during the third week. How much money did she earn?**
\[ 28 \times 8.35 = 233.80 \]
Sandra earned $233.80.
**c. Create a graph showing how much Sandra will earn for working 5, 10, 15, 20, and 25 hours a week.**
**Explanation of the Graph:**
- The graph is set on a standard Cartesian coordinate plane.
- The horizontal axis (x-axis) represents the number of hours worked, marked at intervals of 10: 10, 20, 30, 40, 50, 60, 70, 80.
- The vertical axis (y-axis) represents the earnings, marked at intervals of 100: 100, 200, 300, 400, 500, 600.
- A point is plotted at (20, 167), indicating the earnings for 20 hours of work.
- Draw a straight line through the origin (0, 0) and the plotted points, which represents the direct variation relationship.
- This line can be used to find earnings for any given number of hours by following the line from the x-axis (hours) to the y-axis (earnings).
The relationship between hours worked and earnings is linear, indicating a constant rate of change.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9835c15-0093-41c2-ae19-14f94d022ea4%2F3050f5a9-159c-47d9-8036-4beeafcd47c1%2Fb1fqcm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Lesson 4: Direct Variation**
**Rate of Change**
**18. Practice Problem**
Sandra was hired as a part-time office assistant. The amount of money she earns in a week is proportional to the number of hours she works during the week. She earned $167 for working 20 hours during her first week on the job. During the second week, she worked 35 hours and earned $292.25.
**a. Identify the constant of proportionality in this situation.**
\[ \frac{167}{20} = 8.35 \]
\[ \frac{292.25}{35} \approx 8.35 \]
**b. Sandra worked for 28 hours during the third week. How much money did she earn?**
\[ 28 \times 8.35 = 233.80 \]
Sandra earned $233.80.
**c. Create a graph showing how much Sandra will earn for working 5, 10, 15, 20, and 25 hours a week.**
**Explanation of the Graph:**
- The graph is set on a standard Cartesian coordinate plane.
- The horizontal axis (x-axis) represents the number of hours worked, marked at intervals of 10: 10, 20, 30, 40, 50, 60, 70, 80.
- The vertical axis (y-axis) represents the earnings, marked at intervals of 100: 100, 200, 300, 400, 500, 600.
- A point is plotted at (20, 167), indicating the earnings for 20 hours of work.
- Draw a straight line through the origin (0, 0) and the plotted points, which represents the direct variation relationship.
- This line can be used to find earnings for any given number of hours by following the line from the x-axis (hours) to the y-axis (earnings).
The relationship between hours worked and earnings is linear, indicating a constant rate of change.
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