Worksheet 1 on linear equations in one variable featuring multiple-choice problems with solutions.

Problem Analysis:

The worksheet focuses on solving linear equations in one variable. Each question involves setting up an equation based on a given scenario and solving for the unknown variable \( x \). Let's solve each problem step by step.

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Question 1:

Write the equation and solve. \( \frac{1}{5} \) of a number is 60. What is the number?

#### Solution:
1. Let the number be \( x \).
2. According to the problem, \( \frac{1}{5} \) of the number is 60. This can be written as:
\[
\frac{1}{5}x = 60
\]
3. To solve for \( x \), multiply both sides of the equation by 5:
\[
x = 60 \times 5
\]
\[
x = 300
\]

#### Correct Answer:
\[
\boxed{B}
\]

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Question 2:

Write the equation and solve. \( \frac{1}{10} \) of a number \( x \) is 49. What is \( x \)?

#### Solution:
1. Let the number be \( x \).
2. According to the problem, \( \frac{1}{10} \) of the number is 49. This can be written as:
\[
\frac{1}{10}x = 49
\]
3. To solve for \( x \), multiply both sides of the equation by 10:
\[
x = 49 \times 10
\]
\[
x = 490
\]

#### Correct Answer:
\[
\boxed{A}
\]

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Question 3:

Write the equation and solve. 10% of a number \( x \) is 63. What is \( x \)?

#### Solution:
1. Let the number be \( x \).
2. According to the problem, 10% of the number is 63. This can be written as:
\[
10\% \text{ of } x = 63
\]
Since 10% is equivalent to \( \frac{10}{100} \) or \( 0.1 \), the equation becomes:
\[
0.1x = 63
\]
3. To solve for \( x \), divide both sides of the equation by 0.1:
\[
x = \frac{63}{0.1}
\]
\[
x = 630
\]

#### Correct Answer:
\[
\boxed{D}
\]

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Question 4:

Write the equation and solve. \( \frac{1}{6} \) of the length of a stick is 5 cm. What is the length of the stick if it is \( x \)?

#### Solution:
1. Let the length of the stick be \( x \).
2. According to the problem, \( \frac{1}{6} \) of the length of the stick is 5 cm. This can be written as:
\[
\frac{1}{6}x = 5
\]
3. To solve for \( x \), multiply both sides of the equation by 6:
\[
x = 5 \times 6
\]
\[
x = 30
\]

#### Correct Answer:
\[
\boxed{A}
\]

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Final Answers:

1. \(\boxed{B}\)
2. \(\boxed{A}\)
3. \(\boxed{D}\)
4. \(\boxed{A}\)

These are the correct answers to the multiple-choice questions. Each step involves setting up the equation based on the given information and solving for the unknown variable \( x \).