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

Question

3829 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-30T19:03:44

See the solution process below:

First, let the age of Leah be represented by $l$ $l$ and the age of $tan y a$ $Tanya$ be represented by $t$ $t$ :

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

$t = l + 12$ $t = l + 12$

We can write the age difference three years ago as:

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

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

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

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

$l + 9 = (5 \cdot l) - (5 \cdot 3)$ $l + 9 = (5 * l) - (5 * 3)$

$l + 9 = 5 l - 15$ $l + 9 = 5l - 15$

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

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

$24 = (- 1 + 5) l$ $24 = (-1 + 5)l$

$24 = 4 l$ $24 = 4l$

$\frac{24}{4} = \frac{4 l}{4}$ $24/color(red)(4) = (4l)/color(red)(4)$

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

$6 = l$

$l = 6$

Leah is 6 years old.