Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Select the correct answer.

Jessica is 5 years older than her sister Jenna. Jenna tells her sister that in 5 years, she will be as old as Jessica was 5 years ago. If Jenna's age is [tex]$x$[/tex], which equation represents the situation? How many solutions does the equation have?

A. [tex]$x+5=(5-x)-5$[/tex], which has one solution
B. [tex][tex]$x+5=(x+5)-5$[/tex][/tex], which has infinitely many solutions
C. [tex]$x+5=(x+5)-5$[/tex], which has no solution
D. [tex]$x+5=(5-x)-5$[/tex], which has infinitely many solutions
E. [tex][tex]$(x+5)+5=(x+5)+5$[/tex][/tex], which has infinitely many solutions

Sagot :

GinnyAnswer
To solve this problem, let's analyze the information step by step.

1. Understanding the Ages:
- Jessica is 5 years older than her sister Jenna.
- Let's denote Jenna's current age as [tex]\( x \)[/tex].

2. Express Jessica's Current Age:
- Since Jessica is 5 years older than Jenna, we can write:
[tex]\[ \text{Jessica's age} = x + 5 \][/tex]

3. Ages in 5 Years:
- In 5 years, Jenna's age will be:
[tex]\[ x + 5 \][/tex]
- In 5 years, Jessica's age will be:
[tex]\[ (x + 5) + 5 = x + 10 \][/tex]

4. Jessica's Age 5 Years Ago:
- 5 years ago, Jessica's age was:
[tex]\[ (x + 5) - 5 = x \][/tex]

5. The Given Condition:
- Jenna tells Jessica that in 5 years, she (Jenna) will be as old as Jessica was 5 years ago.
- This age condition can be written as:
[tex]\[ \text{Jenna's age in 5 years} = \text{Jessica's age 5 years ago} \][/tex]
[tex]\[ x + 5 = x \][/tex]

Now let's analyze the answer choices:

A. [tex]\( x + 5 = (5 - x) - 5 \)[/tex], which has one solution:
- This option does not match the condition we derived.

B. [tex]\( x + 5 = (x + 5) - 5 \)[/tex], which has infinitely many solutions:
- Simplify the right-hand side: [tex]\( (x + 5) - 5 = x \)[/tex]
- We get: [tex]\( x + 5 = x \)[/tex]
- This equation simplifies to an identity, which means it is always true regardless of the value of [tex]\( x \)[/tex]. Therefore, this choice is correct and it has infinitely many solutions.

C. [tex]\( x + 5 = (x + 5) - 5 \)[/tex], which has no solution:
- As we analyzed above, this equation [tex]\( x + 5 = x \)[/tex] has infinitely many solutions, not no solution. So this option is incorrect.

D. [tex]\( x + 5 = (5 - x) - 5 \)[/tex], which has infinitely many solutions:
- This option does not match the condition we derived and the equation is not equivalent to [tex]\( x + 5 = x \)[/tex].

E. [tex]\( (x + 5) + 5 = (x + 5) + 5 \)[/tex], which has infinitely many solutions:
- This equation is not relevant to the condition given in the problem.

After analyzing all of the options, the correct answer is:

B. [tex]\( x + 5 = (x + 5) - 5 \)[/tex], which has infinitely many solutions.
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.