Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Wang Lei would like to build a 144ft^(2) rectangular garden. He plans to enclose this area with exactly 50ft of fencing. Which of the following equations could be used to find the width, x, of Wang Lei's garden? Choose 1 answer: (A) x(72-x)=50 (B) x(25-x)=144 (C) x(144-2x)=50 (D) x(50-2x)=144

Wang Lei would like to build a 144ft2 144 \mathrm{ft}^{2} rectangular garden. He plans to enclose this area with exactly 50ft 50 \mathrm{ft} of fencing. Which of the following equations could be used to find the width, x x , of Wang Lei's garden?\newlineChoose 11 answer:\newline(A) x(72−x)=50 x(72-x)=50 \newline(B) x(25−x)=144 x(25-x)=144 \newline(C) x(144−2x)=50 x(144-2 x)=50 \newline(D) x(50−2x)=144 x(50-2 x)=144

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Solve a system of equations using any method: word problemsright chevron icon

Full solution

Q. Wang Lei would like to build a 144ft2 144 \mathrm{ft}^{2} rectangular garden. He plans to enclose this area with exactly 50ft 50 \mathrm{ft} of fencing. Which of the following equations could be used to find the width, x x , of Wang Lei's garden?\newlineChoose 11 answer:\newline(A) x(72−x)=50 x(72-x)=50 \newline(B) x(25−x)=144 x(25-x)=144 \newline(C) x(144−2x)=50 x(144-2 x)=50 \newline(D) x(50−2x)=144 x(50-2 x)=144
  1. Understanding the Rectangle Area: Understand the relationship between the area of a rectangle and its sides.\newlineThe area of a rectangle is given by the product of its length and width. Wang Lei's garden has an area of 144144 square feet. If we denote the width as xx and the length as yy, then the area can be represented as x×y=144x \times y = 144.
  2. Relating Perimeter to Fencing: Relate the perimeter of the rectangle to the fencing. The perimeter of a rectangle is given by 22 times the sum of its length and width. Wang Lei has 5050 feet of fencing, which means the perimeter of the garden is 5050 feet. This can be represented as 2x+2y=502x + 2y = 50.
  3. Solving for a Variable: Solve the perimeter equation for one of the variables.\newlineTo find an equation involving only xx, we can solve the perimeter equation for yy. Dividing the entire equation by 22 gives us x+y=25x + y = 25. Now, solve for yy: y=25−xy = 25 - x.
  4. Substituting into the Area Equation: Substitute the expression for yy into the area equation.\newlineNow that we have yy in terms of xx, we can substitute it into the area equation: x×(25−x)=144x \times (25 - x) = 144. This equation relates the width xx to the area of the garden.
  5. Matching the Derived Equation: Check the given options to see which one matches the derived equation.\newlineComparing the derived equation x(25−x)=144x(25 - x) = 144 with the given options, we see that option (B) matches the equation we found.

More problems from Solve a system of equations using any method: word problems

Question
Solve using elimination.\newlinex+6y=−15x + 6y = -15\newline−2x+6y=12-2x + 6y = 12\newline(_,_)(\_,\_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Is (1,1)(1,1) a solution to this system of equations?\newline8x+y=98x + y = 9\newline6x+12y=186x + 12y = 18\newlineChoices:\newline[[yes]\newline[no]]
Get tutor helpright-arrow

Posted 5 months ago

Question
How many solutions does the system of equations below have?\newliney = x − 77\newliney = x − 77\newlineChoices:\newline[A]no solution\text{[A]no solution}\newline[B]one solution\text{[B]one solution}\newline[C]infinitely many solutions\text{[C]infinitely many solutions}
Get tutor helpright-arrow

Posted 7 months ago

Question
Which describes the system of equations below?\newliney=17x−10y = \frac{1}{7}x - 10\newliney=17x−10y = \frac{1}{7}x - 10\newlineChoices:\newline[A]consistent and independent\text{[A]consistent and independent}\newline[B]consistent and dependent\text{[B]consistent and dependent}\newline[C]inconsistent\text{[C]inconsistent}
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve using substitution.\newliney=−5y = -5\newline−4x+3y=17-4x + 3y = 17\newline(_____, _____)
Get tutor helpright-arrow

Posted 5 months ago

Question
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineLast Wednesday, two friends met up after school to read the book they were both assigned in Literature class. Bryan can read 22 pages per minute, and he had already read 9898 pages. Jayla, who has a reading speed of 33 pages per minute, had read 4848 pages. Eventually they had read the same number of pages. How long did that take? How many pages had each of them read?\newlineAfter ____\_\_\_\_ minutes, Bryan and Jayla had each read ____\_\_\_\_ pages.
Get tutor helpright-arrow

Posted 5 months ago

Question
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineAt the Castroville Ice Cream Parlor, one group of friends ordered 11 small serving of ice cream and 33 large servings of ice cream for 2020. Another group of friends ordered 11 small serving of ice cream and 44 large servings of ice cream for 2626. How much does the ice cream cost?\newlineThe ice cream costs `\$`_____ for a small serving and `\$`_____ for a large serving.
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve.\newliney=−1y = -1\newline−2x−4y=8-2x - 4y = 8\newline(_____ , _____)
Get tutor helpright-arrow

Posted 7 months ago

Question
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineThere are two mystery numbers. The sum of 33 times the first number and 33 times the second number is −18-18. The sum of 22 times the first number and 33 times the second number is −13-13. What are the two numbers?\newlineThe first number is ______ , and the second number is ______.
Get tutor helpright-arrow

Posted 7 months ago

Question
A teacher purchased 300300 colored pencils for an upcoming project. The pencils she ordered come in packs of 2020 and packs of 3030. She ordered 1414 packs in all. Write a system of equations to find the number of 2020-pencil packs (x)(x) and 3030-pencil packs (y)(y) the art teacher ordered.
Get tutor helpright-arrow

Posted 8 months ago

View all (187)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant