Question

Madison is 16 years older than Chris.In 6 years,Madison will be double Chris’s age.how old is each now?

Answer 1

Let m be the present age of Madison and c be the present age of Chris.

Since Madison is 16 years older than Chris, the age of Madison can be expressed as,

`m=c+16\text{ ---(1)}`

After 6 years, the age of Madison will be m+6 and the age of Chris will be c+6.

Since it is given that Madison will be double Chris’s age in 6 years, we can write

`m+6=2(c+6)\text{ ---(2)}`

Plug in equation (1) in equation (2) and solve.

`\begin{gathered} c+16+6=2(c+6) \\ c+22=2c+2*6 \\ c+22=2c+12 \\ c-2c=12-22 \\ -c=-10 \\ c=10 \end{gathered}`

Substitute c=10 in equation (1) to find m.

`\begin{gathered} m=10+16 \\ m=26 \end{gathered}`

Therefore, the present age of Madison is 26 years and the age of Chris is 10 years.