Question

Choose what the expressions below best represent within the context of the word problem. Tom is 8 years older than Jane. Five years ago Tom was three times as old as Jane. How old is Jane now?

a) Jane−13
b) Jane+13
c) Tom+13
d) Tom−13

Answer 1

Jane is 9 years old now.

Step-by-step explanation:

To solve this problem, we can set up equations using the given information. Let Jane's age be represented as J and Tom's age be represented as T. From the first sentence, we know that T = J + 8. Now, from the second sentence, we can set up the equation T - 5 = 3(J - 5). Simplifying this equation gives T - 5 = 3J - 15. Substituting T with J + 8, we get J + 8 - 5 = 3J - 15. Solving this equation will give us Jane's age.

Combining like terms, we get J + 3 = 3J - 15. Subtracting J from both sides, we get 3 = 2J - 15. Moving the constant term to the other side, we get 2J = 18. Dividing both sides by 2, we get J = 9. Therefore, Jane is 9 years old now.