Question

Write and solve the equation and then check your answer.
Four times a number is thirty-two.
Which statements are true? Select the three that apply.


A. The correct equation is m/4 = 32.

B. This is a division problem.

C. To solve the equation, divide both sides by 4.

D. The correct equation is 4m = 32.

E. To solve the equation, multiply both sides by 4.

F. This is a multiplication problem.

Answer 1

To formulate the equation based on the statement "Four times a number is thirty-two," we can define the unknown number as \( m \). The phrase "four times a number" translates mathematically to \( 4m \), and "is thirty-two" indicates that this expression equals 32. Thus, we can write the equation:

\[ 4m = 32 \]

**Now, let's solve the equation:**

To find \( m \), we divide both sides by 4:

\[
m = \frac{32}{4} = 8
\]

**Now we will check the answer** by substituting \( m = 8 \) back into the original situation:

Four times the number \( 8 \) is \( 4 \times 8 = 32 \), which is correct.

Now, let's evaluate the statements:

A. **The correct equation is \( m/4 = 32 \).**
- **False.** The correct equation is \( 4m = 32 \).

B. **This is a division problem.**
- **False.** The original statement describes a multiplication operation.

C. **To solve the equation, divide both sides by 4.**
- **True.** We divide both sides of \( 4m = 32 \) by 4.

D. **The correct equation is \( 4m = 32 \).**
- **True.** This is indeed the correct equation.

E. **To solve the equation, multiply both sides by 4.**
- **False.** We divide by 4 to solve for \( m \).

F. **This is a multiplication problem.**
- **True.** The problem originally describes multiplication ("four times a number").

Based on this analysis, the three true statements are:

- C. To solve the equation, divide both sides by 4.
- D. The correct equation is \( 4m = 32 \).
- F. This is a multiplication problem.