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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.
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