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A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 50 pounds and each large box of paper weighs 100 pounds. A total of 20 boxes of paper were shipped weighing 1400 pounds altogether. Graphically solve a system of equations in order to determine the number of small boxes shipped, x, and the number of large boxes shipped, y.

A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 50 pounds and each large box of paper weighs 100 pounds. A total of 20 boxes of paper were shipped weighing 1400 pounds altogether. Graphically solve a system of equations in order to determine the number of small boxes shipped, x, and the number of large boxes shipped, y.

Algebra and Trigonometry (6th Edition)
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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### Problem Statement A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 50 pounds, and each large box of paper weighs 100 pounds. A total of 20 boxes of paper were shipped, weighing 1400 pounds altogether. Graphically solve a system of equations in order to determine the number of small boxes shipped, \( x \), and the number of large boxes shipped, \( y \). ### System of Equations To solve this problem, we need to set up a system of linear equations based on the given conditions: 1. The total number of boxes shipped (both small and large) is 20. \[ x + y = 20 \] 2. The total weight of all the boxes shipped is 1400 pounds. \[ 50x + 100y = 1400 \] Where: - \( x \) is the number of small boxes (each weighing 50 pounds). - \( y \) is the number of large boxes (each weighing 100 pounds). ### Steps to Solve Graphically 1. **Rewrite the equations in terms of \( y \):** For the first equation: \[ y = 20 - x \] For the second equation: \[ 50x + 100y = 1400 \] Simplify it by dividing every term by 50: \[ x + 2y = 28 \] Solve for \( y \): \[ 2y = 28 - x \] \[ y = 14 - \frac{x}{2} \] 2. **Graph the equations:** - Plot the line \( y = 20 - x \). This line will pass through the points (0, 20) and (20, 0). - Plot the line \( y = 14 - \frac{x}{2} \). This line will pass through the points (0, 14) and (28, 0). 3. **Find the intersection point:** - Graphically find the point where these two lines intersect. This point will provide the values of \( x \) and \( y \) that satisfy both equations. The intersection point is the solution to the system. ### Conclusion By solving the system graphically, we can determine the
Transcribed Image Text:### Problem Statement A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 50 pounds, and each large box of paper weighs 100 pounds. A total of 20 boxes of paper were shipped, weighing 1400 pounds altogether. Graphically solve a system of equations in order to determine the number of small boxes shipped, \( x \), and the number of large boxes shipped, \( y \). ### System of Equations To solve this problem, we need to set up a system of linear equations based on the given conditions: 1. The total number of boxes shipped (both small and large) is 20. \[ x + y = 20 \] 2. The total weight of all the boxes shipped is 1400 pounds. \[ 50x + 100y = 1400 \] Where: - \( x \) is the number of small boxes (each weighing 50 pounds). - \( y \) is the number of large boxes (each weighing 100 pounds). ### Steps to Solve Graphically 1. **Rewrite the equations in terms of \( y \):** For the first equation: \[ y = 20 - x \] For the second equation: \[ 50x + 100y = 1400 \] Simplify it by dividing every term by 50: \[ x + 2y = 28 \] Solve for \( y \): \[ 2y = 28 - x \] \[ y = 14 - \frac{x}{2} \] 2. **Graph the equations:** - Plot the line \( y = 20 - x \). This line will pass through the points (0, 20) and (20, 0). - Plot the line \( y = 14 - \frac{x}{2} \). This line will pass through the points (0, 14) and (28, 0). 3. **Find the intersection point:** - Graphically find the point where these two lines intersect. This point will provide the values of \( x \) and \( y \) that satisfy both equations. The intersection point is the solution to the system. ### Conclusion By solving the system graphically, we can determine the
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