Worksheet-1 featuring multiple-choice questions on writing and solving linear equations in one variable.

Problem Analysis and Solution

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

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#### Question 1:
Problem Statement:
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:
\[
x = 60 \times 5 = 300
\]

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

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#### Question 2:
Problem Statement:
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:
\[
x = 49 \times 10 = 490
\]

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

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#### Question 3:
Problem Statement:
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:
\[
0.1x = 63
\]
or equivalently,
\[
\frac{10}{100}x = 63 \quad \text{(since 10% = 10/100)}
\]
3. To solve for \( x \), divide both sides of the equation by 0.1 (or multiply by 10):
\[
x = \frac{63}{0.1} = 630
\]

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

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#### Question 4:
Problem Statement:
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:
\[
x = 5 \times 6 = 30
\]

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

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Final Answers:

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

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Explanation:

Each question involves translating the word problem into a mathematical equation and then solving for the unknown variable \( x \). The key steps are:
1. Identify the variable and set up the equation based on the problem statement.
2. Solve the equation using basic algebraic operations (multiplication, division, etc.).
3. Verify the solution by substituting it back into the original equation.

This approach ensures accuracy and clarity in solving linear equations in one variable.