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

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Answer 1 · 2017-04-30T19:03:44

See the solution process below:

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.