Question

This year, Antonia is half the age of her 64 year old mother. How old will Antonia be when her mother is 79 years old?

Answer 1

Let Antonia's current age be \( A \) and her mother's current age be \( M \). We know that:

\[
M = 64
\]

Additionally, we know that:

\[
A = \frac{M}{2} = \frac{64}{2} = 32
\]

So, Antonia is currently 32 years old.

Next, we want to find out how old Antonia will be when her mother is 79 years old. The difference in age between Antonia and her mother is:

\[
M - A = 64 - 32 = 32
\]

This means Antonia will always be 32 years younger than her mother. When her mother is 79 years old:

\[
\text{Age of Antonia} = 79 - 32 = 47
\]

Thus, when her mother is 79 years old, Antonia will be \( \boxed{47} \) years old.