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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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.

Explanation:

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

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

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

$m = s + 11$ $m = s + 11$

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

#m + 8 = 2(s + 8)

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

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

$s + 19 = 2 s + 16$ $s + 19 = 2s + 16$

$s - s + 19 - 16 = 2 s - s + 16 - 16$ $s - s + 19 - 16 = 2s - s + 16 - 16$

$0 + 3 = s$ $0 + 3 = s$

$s = 3$ $s = 3$

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

$m = 3 + 11$ $m = 3 + 11$

$m = 14$ $m = 14$

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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?

1 Answer

Explanation:

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