Respuesta :
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.
[tex]M=K+4[/tex]- Alexis is twice as old as Mona.
[tex]A=2M[/tex]- The sum of their ages is 48.
[tex]M+K+A=48[/tex]We can see that we have a system of three equations
[tex]\begin{cases}M=K+4\ldots(1) \\ A=2M\ldots(2) \\ M+K+A=48\ldots(3)\end{cases}[/tex]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)
[tex]\begin{gathered} M=K+4 \\ K=M-4 \end{gathered}[/tex]- Equation (2)
[tex]\begin{gathered} A=2M \\ \end{gathered}[/tex]Then, we must replace the value of K and A in the equation (3)
[tex]\begin{gathered} M+K+A=48 \\ M+(M-4)+2M=48 \end{gathered}[/tex]Simplifying,
[tex]\begin{gathered} M+M-4+2M=48 \\ 2M-4+2M=48 \\ 4M=48+4 \\ M=13 \end{gathered}[/tex]Finally, we must replace M to find A and K
[tex]\begin{gathered} K=M-4 \\ K=13-4 \\ K=9 \end{gathered}[/tex][tex]\begin{gathered} A=2M \\ A=2(13) \\ A=26 \end{gathered}[/tex]So,
Mona is 13 years old.
Karly is 9 years old.
Alexis is 26 years old.
