Question

Alison is now three times as old as Jeremy, but 5 years ago, she was 5 times as old as he was. How old is Alison now?

Answer 1

Using a system of equations, we determine that Jeremy is 10 years old. Then, by knowing the first equation A=3J, we find that Alison is currently 30 years old.

Step-by-step explanation:

Alison is currently three times as old as Jeremy. If we let A represent Alison's current age and J represent Jeremy's current age, we can write this relationship as:

A = 3J

Additionally, five years ago, Alison was five times as old as Jeremy was at that time. If we subtract 5 years from their current ages, we have:

(A - 5) = 5(J - 5)

Now we have two equations:

1. A = 3J
2. A - 5 = 5J - 25

Using substitution, we can replace A in the second equation with 3J from the first equation:

3J - 5 = 5J - 25

Solving for J:

3J - 5J = -25 + 5

-2J = -20

J = 10

Now that we know Jeremy's age, we use the first equation to find Alison's age:

A = 3 × 10

A = 30

Hence, Alison is 30 years old now.