Question

Abe is 4 years old, and he is one third of Sonia's age. In how many years will he be more than one half of Sonia's age at that time?

Answer 1

In 5 years he'll be more than half Sonia's age

Step-by-step 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:

`\begin{gathered} (1)/(3)x=4 \\ x=3\cdot4 \\ x=12 \end{gathered}`

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:

`(x-8)=(1)/(2)x`

Solving for x, we'll know Sonia's age at the time:

`\begin{gathered} x-(1)/(2)x=8 \\ (1)/(2)x=8 \\ x=2\cdot8 \\ x=16 \end{gathered}`

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):

`\begin{gathered} 9>(1)/(2)17 \\ 9>8.5 \end{gathered}`

If Abe is 4 years old now, then in 5 years he'll be more than half Sonia's age