Question

A larger number is 2 more than 4 times a smaller number. The larger number is also 8 more than 2 times the smaller number.

1. Define the variables: x = smaller number and y = larger number

2. Identify the key words: more than (addition), times (multiplication), is (equals)

3. Write the equations.

Which equation represents a larger number that is 2 more than 4 times a smaller number?

Which equation represents a larger number that is 8 more than 2 times a smaller number?

Answer 1

Let's define the variables and write the equations based on the statements provided.

1. **Define the variables:**
- Let \( x \) be the smaller number.
- Let \( y \) be the larger number.

2. **Identify the key words:**
- "more than" indicates addition.
- "times" indicates multiplication.
- "is" indicates equals.

3. **Write the equations:**
- **Equation 1:** The larger number is 2 more than 4 times the smaller number.
\[
y = 4x + 2
\]

- **Equation 2:** The larger number is 8 more than 2 times the smaller number.
\[
y = 2x + 8
\]

**Summary of the equations:**
- The first equation representing a larger number that is 2 more than 4 times a smaller number is:
\[
y = 4x + 2
\]

- The second equation representing a larger number that is 8 more than 2 times a smaller number is:
\[
y = 2x + 8
\]