Question

An old lady is 5 times as old as a girl. Six years ago she was 8 times as old as the girl. How old they now

Answer 1

Let's denote the current age of the girl as \( g \) and the current age of the old lady as \( l \).

From the problem, we have the following two relationships:

1. The old lady is currently 5 times as old as the girl:
\[
l = 5g
\]

2. Six years ago, the old lady was 8 times as old as the girl:
\[
l - 6 = 8(g - 6)
\]

Now let's substitute the first equation into the second equation:

Substituting \( l \) into the second equation gives:
\[
5g - 6 = 8(g - 6)
\]

Expanding the right side:
\[
5g - 6 = 8g - 48
\]

Now, let's rearrange the equation to isolate \( g \):
\[
5g - 8g = -48 + 6
\]
\[
-3g = -42
\]
\[
g = 14
\]

Now that we have the age of the girl, we can find the age of the old lady using the first equation:
\[
l = 5g = 5 \times 14 = 70
\]

So the current ages are:
- The girl is **14 years old**.
- The old lady is **70 years old**.