Question

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

Answer 1

Charles = 24 years

Ann = 8 years

Step-by-step explanation:

We were given that:

Charles is 16 years older than Ann

In 8 years, Charles will be twice as old as Ann

We will develop the following equations from the details above:

Let Charles' age be represented by ''c''

Let Ann's age be represented by ''a''

`\begin{gathered} Now\colon c=a+16----------1 \\ 8years\colon c+8=2(a+8)------2 \end{gathered}`

We will proceed to solve the equations simultaneously, we have:

`\begin{gathered} c=a+16----------1 \\ c+8=2(a+8)\Rightarrow c+24=2a+16------2 \\ c+8=2a+16------2 \\ Substituting\text{ equation 1 into equation 2, we have:} \\ a+16+8=2a+16 \\ a+24=2a+16 \\ \text{Subtract ''16'' from both sides, we have:} \\ a+8=2a \\ \text{Subtract ''a'' from both sides, we have:} \\ 8=a \\ a=8 \\ \text{Substitute ''a'' into equation 1, we have:} \\ c=8+16 \\ c=24 \\ \\ \therefore a=8,c=24 \end{gathered}`

Hence, Charles is 24 years old & Ann is 8 years old