Question

Mona is four years older than Karly.Alexis is twice as old as Mona. Thesum of their ages is 48. How old iseach girl?

Answer 1

We know that:

- Mona is four years older than Karly.

- Alexis is twice as old as Mona.

- The sum of their ages is 48.

To represent the situation we must use variables.

- M represents the age of Mona.

- K represents the age of Karly.

- A represent the age of Alexis.

Now, we must represent with the varibles the three data that the exercise gives us.

- Mona is four years older than Karly.

`M=K+4`

- Alexis is twice as old as Mona.

`A=2M`

- The sum of their ages is 48.

`M+K+A=48`

We can see that we have a system of three equations

`\begin{cases}M=K+4\ldots(1) \\ A=2M\ldots(2) \\ M+K+A=48\ldots(3)\end{cases}`

We can see that equation (3) relates the 3 variables, and we can also see that equations (1) and (2) have in common the variable M.

So, now we must leave in terms of M equations (1) and (2)

- Equation (1)

`\begin{gathered} M=K+4 \\ K=M-4 \end{gathered}`

- Equation (2)

`\begin{gathered} A=2M \\ \end{gathered}`

Then, we must replace the value of K and A in the equation (3)

`\begin{gathered} M+K+A=48 \\ M+(M-4)+2M=48 \end{gathered}`

Simplifying,

`\begin{gathered} M+M-4+2M=48 \\ 2M-4+2M=48 \\ 4M=48+4 \\ M=13 \end{gathered}`

Finally, we must replace M to find A and K

`\begin{gathered} K=M-4 \\ K=13-4 \\ K=9 \end{gathered}`
`\begin{gathered} A=2M \\ A=2(13) \\ A=26 \end{gathered}`

So,

Mona is 13 years old.

Karly is 9 years old.

Alexis is 26 years old.