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.