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Sagot :
Let's call M the present age of Maya, and F the present age of Fiona.
Three years ago Maya was eleven times as old as Fiona. At that time, Maya's age was M-3, and Fiona's age was F-3. Thus, we have:
[tex]M-3=11(F-3)[/tex]Also, in four years Maya will be four times as old as Fiona. At that time, Maya's age will be M+4, and Fiona's age will be F+4. Thus, we have:
[tex]M+4=4(F+4)[/tex]Now, we need to solve the system of those two equations to find M and F. Subtracting the second equation from the first, we obtain:
[tex]\begin{gathered} M-3-(M+4)=11F-33-(4F+16) \\ \\ M-3-M-4=(11-4)F-33-16 \\ \\ -7=7F-49 \\ \\ -7+49=7F-49+49 \\ \\ 42=7F \\ \\ \frac{42}{7}=\frac{7F}{7} \\ \\ 6=F \\ \\ F=6 \end{gathered}[/tex]Now, we can use the above result to find M:
[tex]\begin{gathered} M+4=4(6+4) \\ \\ M+4=40 \\ \\ M+4-4=40-4 \\ \\ M=36 \end{gathered}[/tex]Therefore, now Maya is 40 years old and Fiona is 6 years old.
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