Final answer:
In summary, the age word problem is solved by letting x represent Jane's current age, after which an equation is formulated based on the given relationships. By solving the equation, we find that Jane is currently 9 years old, and therefore, the correct option is A) x represents Jane's age.
Step-by-step explanation:
We are given a word problem that involves forming a set of equations based on the information provided. The problem is:
Tom is 8 years older than Jane. Five years ago, Tom was three times as old as Jane. How old is Jane now?
Formulating the equations
Let's use x to represent Jane's current age. Since Tom is 8 years older than Jane, Tom's current age would be represented as x + 8. Now, we take into consideration the second part of the information: five years ago, the relationship between their ages was such that Tom was three times as old as Jane. If we subtract five from their current ages, we get the following equations:
According to the problem, five years ago Tom was three times as old as Jane. Therefore, this relationship can be expressed as:
Solving the equation
Now we will solve for x:
Therefore, Jane is currently 9 years old.
The correct option from the given choices, based on this problem, is A) x represents Jane's age.