Mark is 11 years older than his sister. In 8 years he he will be twice as old as she will be then. How old are they now?

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Answer 1 · 2016-12-13T04:42:54

Mark is 14 years old and his sister is 3 years old.

Let's call Mark's age now #m#

Let's call his sister's age now #s#

We know now Mark is 11 years older than his sister or:

#m = s + 11#

In 8 years, so #m + 8# and #s + 8# years. So we can write:

#m + 8 = 2(s + 8)

We already have the first equation in terms of #m#. So, we can substitute #s + 11# for #m# in the second equation and solve for #s#:

#s + 11 + 8 = 2(s + 8)#

#s + 19 = 2s + 16#

#s - s + 19 - 16 = 2s - s + 16 - 16#

#0 + 3 = s#

#s = 3#

We can now substitute #3# for #s# in the first equation and calculate #m#:

#m = 3 + 11#

#m = 14#