Word problem - linear equation.

In summary, the conversation is about determining the dimensions of a rectangular swimming pool that is surrounded by a cement walkway. The pool's length is twice its width, and the walkway has an area of 748 ft^2. By setting up an equation, the width of the pool is found to be 28.5 ft. However, the book's answer is 30 ft, and 60 ft, which would result in a larger area for the walkway. The individual asking for help agrees with the calculations but questions the discrepancy in the book's answer.
  • #1
paulmdrdo1
385
0
please help me with this problem

please use single variable only.

The length of a rectangular swimming pool is twice its width. The pool is surrounded by a cement walk 4ft wide. If the area of the walk is 748 ft^2, determine the dimensions of the pool.

let x = width of the pool
2x = length of the pool

the dimensions of the pool and cement walk combined

x+8 = width
2x+8 = length

the area of the pool plus the area of the cement walk is equal to the whole area.

$(2x+8)(x+8)=748+2x^2$

$x= 28.5$

the dimensions of the pool is 28.5 ft by 57 ft.

but the answer in my book is 30 ft. by 60 ft. why is that? where did I miss?

regards!

please use one variable only.
 
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  • #2
The area of the walk (using your variables) is:

\(\displaystyle 2(4x+4(2x+8))=748\)

\(\displaystyle 4(6x+16)=748\)

\(\displaystyle 6x+16=187\)

\(\displaystyle 6x=171\)

\(\displaystyle x=28.5\)

I agree with you.
 
  • #3
If the answer is 30 ft x 60 ft then the area of the walk would be 784, not 748. Did you read the question correctly?
 

1. What is a linear equation?

A linear equation is an algebraic equation in which the highest power of the variable is 1. It can be written in the form of y = mx + b, where m is the slope and b is the y-intercept.

2. How do you solve a word problem involving a linear equation?

To solve a word problem involving a linear equation, you first need to identify the variables and write them in terms of x and y. Then, use the given information to form an equation and solve for the missing variable using algebraic methods such as substitution or elimination.

3. What is the importance of word problems involving linear equations?

Word problems involving linear equations are important because they allow us to apply mathematical concepts to real-life situations. They also help us develop critical thinking and problem-solving skills.

4. What are some common mistakes to avoid when solving word problems involving linear equations?

Some common mistakes to avoid when solving word problems involving linear equations include misinterpreting the given information, using the wrong formula or equation, and making calculation errors. It is important to carefully read the problem and double-check your work to avoid these mistakes.

5. How can linear equations be applied in the real world?

Linear equations can be applied in various fields such as engineering, economics, and physics. They can be used to model and analyze real-world situations involving relationships between two variables, such as distance vs. time or cost vs. quantity.

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