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?

Question

5849 views around the world

You can reuse this answer
Creative Commons License

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#