### Problem StatementA 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 EquationsTo 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 Graphically1. **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.### ConclusionBy solving the system graphically, we can determine the

In this question, we will compute the system of equations and solve them graphically.

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)

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,...

See similar textbooks

Related questions

Q: How many gallons of 30% alcohol and 60% alcohol are needed to obtain a 20-gallon mixture which is…

A: Let x be the number of gallons of 30% alcohol. So, (20-x) will be the number of gallons of 60%…

Q: Allison owns a trucking company. For every truck that goes out, Allison must pay the driver $11 per…

A: A system of linear equations can be solved to find out the unknown variables.

Q: Indicate the solution to the system of linear equations by typing your solution in the boxes…

A: We want to find value of x and y

Q: On tuesday the 8th graders at OWMS sold 75 heart valentine's and 20 jumbo lollipops at lunch and…

Q: A small company took out three different loans totaling $73000 to expand their business. The annual…

A: A small company took out three different loans totalling to expand their business.The annual rate…

Q: Car A travels at an average speed of 65 miles per hour. Car B travels at an average speed of 55…

Q: The bakery at Sam's club makes jumbo cookies and regular cookies. The oven can make at most 200…

A: Let x and y be the be the number of jumbo cookies and regular cookies to be made respectively. So…

Q: Martha is visiting New York City for the first time. Her hotel is on 6th Avenue, which is at point…

Q: At a particular restaurant, each slider has 200 calories and each mini hotdog has 100 calories. A…

Q: The perimeter of a rectangular flower garden is 21 feet. This garden is to be built on the side of a…

A: Given the perimeter of a rectangular flower garden as 21 feet.

Q: You just joined the local arboretum for a flat fee of $82. They charge an extra $31 for each special…

A: Explained below

Q: teacher purchased 18 juice boxes and 32 bottles of water, and spent $19.92. THe other teacher…

Q: two students in the same Spanish class, Tristan and Nancy, plan to get together after school to make…

Question

### 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

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

The product of two consecutive positive odd integers is 399. The two integers are and Enter the smaller integer in the first box.
One alloy contains 15% silver and a second alloy contains 40% silver. How many kilograms of each alloy are needed to make 25 kilograms of 20% of silver alloy. Can you write a system of equations.
The edges of a rectangular plece of plastic sheet are joined together to make a plastic tube. If the area of the plastic sheet is 284 cm", and the volume of the resulting tube is 134 cm³, what are the dimensions of the plastic sheet? Assume the sheet is longer than it is wide Determine the system of equations for this situation. Let x represent the width of the sheet, y represent the length of sheet. A represent the area of the sheet, and V represent the volume of the tube Assume that the width is used to form the circular base of the tube OA. A=xy v=mx² 4x OC. A-xy VaRx OB. A=xy v=Y²x² 4x OD. A=xy yx V=
A total of 243 adults and children are at a movie theater. There are 109 more adults than children in the theater. If a represents the number of adults and b represents the number of children, which system of equations could be used to find the number of adults and the number of children in the theater?
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 6 cubic feet and the volume of each large box is 15 cubic feet. There were 2 more small boxes shipped than large boxes and the total volume of all boxes was 243 cubic feet. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.
Describe the error in solving for one of the variables in the linear system 4x + 2y = 6 and 3x + y = 9