Question

Write and solve the equation that represents the sentence below.

The product of 18 and a number is 109.8.

Which statements are correct? Check all that apply.
It can be solved by using the division property of equality.
It can be solved by using the multiplication property of equality.
The equation should be StartFraction x Over 18 EndFraction = 109.8.
The equation should be 18 x = 109.8.
The answer is 6.1.
The answer is 1,976.4.

Answer 1

To represent the sentence "The product of 18 and a number is 109.8," we can write the equation as:

\[
18x = 109.8
\]

where \( x \) is the unknown number we want to find.

Now, we can solve for \( x \) using the division property of equality. We divide both sides of the equation by 18:

\[
x = \frac{109.8}{18}
\]

Calculating the right side:

\[
x = 6.1
\]

Now, let’s evaluate the statements provided:

1. **It can be solved by using the division property of equality.**
**Correct.** We used division to isolate \( x \).

2. **It can be solved by using the multiplication property of equality.**
**Incorrect.** We used division, not multiplication, to solve for \( x \).

3. **The equation should be StartFraction x Over 18 EndFraction = 109.8.**
**Incorrect.** The equation should be \( 18x = 109.8 \).

4. **The equation should be 18 x = 109.8.**
**Correct.** This is the correct representation of the statement.

5. **The answer is 6.1.**
**Correct.** This is the correct solution for \( x \).

6. **The answer is 1,976.4.**
**Incorrect.** This is not the correct solution.

To summarize, the correct statements are:
- It can be solved by using the division property of equality.
- The equation should be 18 x = 109.8.
- The answer is 6.1.