Question

Charles is 16 years older than his sister Michelle. In 8 years, he will be twice as old as Michelle. How old is each of them now?

Answer 1

Charles is now 24 years old and Michell 8 years old

1) In this problem, let's turn that information into an equation so that we can solve it using Algebra.

2) The first equation is:

Charles: x+16

Michelle: x

After 8 years, since Charles is going to be twice older than Michelle, we'll have:

$\begin{gathered} C=x+16 \\ M=x \\ --- \\ x+16+8=2(x+8) \\ x+24=2x+16 \\ x-2x=-24+16 \\ -x=-8 \\ x=8 \end{gathered}$

Note that we equated the age of Charles plus 8 to the double of x, Michelle's age.

3) Let's now find the age of them now:

$\begin{gathered} C=8+16 \\ C=24 \\ M=8 \end{gathered}$

Plugging back into the first equations, we can see that Charles is now 24 yrs old and Michell 8 yrs old