Q44. - Algebra 1

Question

To allow for a model’s height, a designer is willing to use model that require him to change hems either up or down 2 inches. The length of the skirts is 20 inches.

1. Write an absolute value equation that represents the length of the skirts.
2. What is the range of the length of the skirts?
3. If a 20 inches skirt was fitted for a model that is 5 feet 9 inches tall, will the designer use a 6-foot-tall model?

Step-by-Step Solution

Answer

1. The equation that represents the length of the skirt is $\left|x-20\right|=2$.
2. The second runner’s fastest time is 52 seconds and the slowest time is 54 seconds.
3. The team’s fastest time is 203 seconds and the slowest time is 214 seconds.

Part a. Step 1. Apply the concept of Variables and constant.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Constants: - In any expression or equation constant are the values which is fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Part a. Step 2. Concept of absolute value.

Absolute value: - Absolute value of any quantity simply means a positive value of that quantity.

Example: -

Consider a variable x. Here, x can be both positive or negative but $\left|x\right|$ will always be positive and hence the absolute value. 

Part a. Step 3. Solution along with the given information.

The given length of the skirt is 20 inches and the to change hems either up or down is 2 inches.

Calculate the absolute value.

Let the length of the skirt be x.

The equation that represents the length of the skirt is $\left|x-20\right|=2$.

Hence the equation that represents the length of the skirt is $\left|x-20\right|=2$.

Part b. Step 1. Apply the concept of Variables and constant.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Constants: - In any expression or equation constant are the values which is fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Part b. Step 2. Concept of absolute value.

Absolute value: - Absolute value of any quantity simply means a positive value of that quantity.

Example: -

Consider a variable x. Here, x can be both positive or negative but $\left|x\right|$ will always be positive and hence the absolute value. 

Part b. Step 3. Solution along with the given information.

Given information:

The given length of the skirt is 20 inches and the to change hems either up or down is 2 inches.

Calculate the range of the skirt.

The equation that represents the length of the skirt is $\left|x-20\right|=2$.

 

Case 1: $\left(x-20\right)=2$

 

Add 20 to both sides of the equation.

$\begin{array}{l}x-20+20=2+20\\ x+0=22\\ x=22\end{array}$ 

 

Case 2: $\left(x-20\right)=-2$:

Add 20 to both sides of the equation.

$\begin{array}{l}x-20+20=-2+20\\ x+0=18\\ x=18\end{array}$ 

 

Therefore, the range of the length of the skirt is 18 inches to 22 inches.

Part c. Step 1. Apply the concept of Variables and constant.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Constants: - In any expression or equation constant are the values which is fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Part c. Step 2. Concept of absolute value.

Absolute value: - Absolute value of any quantity simply means a positive value of that quantity.

Example: -

Consider a variable x. Here x can be both positive or negative but $\left|x\right|$ will always be positive and hence the absolute value. 

Part c. Step 3. Solution along with the given information.

The given length of the skirt is 20 inches and the to-change hems either up or down is 2 inches, and the model height is 5 feet 9 inches.

The determination of a 6-foot-tall model is used by the designer or not to be done if a skirt was fitted for a model that is 5 feet 9 inches.

The difference in the model height is

$$\begin{gathered} 6\text{f}-5\text{f }9 \text{inches}=\left(60-57\right) \text{inches} \\ =3 \text{inches} \end{gathered}$$ 

The difference in shirt length is 2 inches.

Thus, the designer will not use a 6-foot-tall model because in height of the model is greater than the difference in the hem length of the skirt.

 

Therefore, the designer will not use a 6-foot-tall model.