How old are Sam and Amy now?

To find out how old Sam and Amy are now, let’s break down the information given in the question.

From the problem, we know that:

• Sam is 4 years younger than Amy.
• Five years ago, Sam was half Amy’s age.

Let’s denote Amy’s current age as A. Since Sam is 4 years younger, we can denote Sam’s current age as S = A – 4.

Now, let’s consider their ages five years ago:

• Amy’s age five years ago: A – 5
• Sam’s age five years ago: S – 5 = (A – 4) – 5 = A – 9

According to the problem, five years ago, Sam was half Amy’s age, which gives us the equation:

A – 9 = 0.5 * (A – 5)

Now let’s solve this equation:

1. Multiply both sides by 2 to eliminate the fraction:
2. 2(A – 9) = A – 5
3. Expand the left side:
4. 2A – 18 = A – 5
5. Now, isolate A:
6. 2A – A = -5 + 18
7. A = 13

Now that we have Amy’s age, we can find Sam’s age:

S = A – 4 = 13 – 4 = 9

So, Amy is currently 13 years old and Sam is 9 years old.