Question

Tanya is 12 years older than Leah. Three years ago, Tanya was five times as old as Leah. How old is Leah?

Answer 1

See the solution process below:

Explanation:

First, let the age of Leah be represented by `l` and the age of `Tanya` be represented by `t`:

The current age differences between Tanya and Leah can be written as:

`t = l + 12`

We can write the age difference three years ago as:

`t - 3 = 5(l - 3)`

We can subsitute `l + 12` from the first equation for `t` in the second equation and solve for `l`:

`t - 3 = 5(l - 3)` becomes:

`(l + 12) - 3 = 5(l - 3)`

`l + 9 = (5 * l) - (5 * 3)`

`l + 9 = 5l - 15`

`-color(red)(l) + l + 9 + color(red)(15) = -color(red)(l) + 5l - 15 + color(red)(15)`

`0 + 24 = -1color(red)(l) + 5l - 0`

`24 = (-1 + 5)l`

`24 = 4l`

`24/color(red)(4) = (4l)/color(red)(4)`

`6 = (color(red)(cancel(color(black)(4)))l)/cancel(color(red)(4))`

`6 = l`

`l = 6`

Leah is 6 years old.