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Sagot :
ANSWER
In 5 years he'll be more than half Sonia's age
EXPLANATION
Let 'x' be Sonia's age. If Abe is 4 years old and that equals to one third of Sonia's age, we can find how old Sonia is:
[tex]\begin{gathered} \frac{1}{3}x=4 \\ x=3\cdot4 \\ x=12 \end{gathered}[/tex]Sonia is 12 years old, so Abe is 8 years younger than her.
Now we want to know when Abe's age will be more than one half of Sonia's age at that time. If x is Sonia's age, then Abe's age is always (x - 8) - because he's 8 years younger:
[tex](x-8)=\frac{1}{2}x[/tex]Solving for x, we'll know Sonia's age at the time:
[tex]\begin{gathered} x-\frac{1}{2}x=8 \\ \frac{1}{2}x=8 \\ x=2\cdot8 \\ x=16 \end{gathered}[/tex]If we want to know when Abe will be more than one half of Sonia's age, this is 9 years old (and Sonia will be 17 years old):
[tex]\begin{gathered} 9>\frac{1}{2}17 \\ 9>8.5 \end{gathered}[/tex]If Abe is 4 years old now, then in 5 years he'll be more than half Sonia's age
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