Let's solve this problem step by step.
1. Understanding the Problem:
- Leticia stretched for 8 minutes.
- She then jogged around the block several times.
- It takes her 6 minutes to run around the block once.
- The total time she spent exercising is 38 minutes.
2. Defining Variables:
- Let [tex]\( x \)[/tex] be the number of times Leticia jogged around the block.
3. Formulating the Equation:
- The total time spent exercising consists of the time stretching plus the time jogging.
- Time spent stretching: 8 minutes.
- Time spent jogging: [tex]\( 6 \times x \)[/tex] minutes (since it takes 6 minutes per jog around the block).
Therefore, the total exercise time can be written as:
[tex]\[
8 + 6x = 38
\][/tex]
4. Solving the Equation:
- Subtract 8 from both sides of the equation to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
6x = 38 - 8
\][/tex]
[tex]\[
6x = 30
\][/tex]
- Divide both sides by 6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{30}{6}
\][/tex]
[tex]\[
x = 5
\][/tex]
Thus, Leticia jogged around the block 5 times.
### Choosing the Correct Answers
Based on the steps above, we have:
- The equation that models this situation is [tex]\( 8 + 6x = 38 \)[/tex] (Answer A).
- The correct answer is that Leticia jogged around the block 5 times (Answer B).
Therefore, the correct answers are:
- A. Equation: [tex]\( 8 + 6x = 38 \)[/tex]
- B. Answer: 5 times around the block
