Laura and her grandmother Ana have just discovered that last year their ages were divisible by 8 and that next year they will be divisible by 7. Grandma Ana is not yet a centenarian. What is Laura's age?
Next year, Laura and her grandmother will be two years older than they were last year. Therefore, their ages last year are multiples of 8 that, when added to 2, give multiples of 7. Let's find these numbers.

$$
\begin{array}{rllllllllllll}
\text { multiples of } 7: & 7 & 14 & 21 & 28 & 35 & 42 & 49 & 56 & 63 & \ldots & 98 & \ldots \\
\text { (multiples of } 7 \text { ) }-2: & 5 & 12 & 19 & 26 & 33 & 40 & 47 & 54 & 61 & \ldots & 96 & \ldots
\end{array}
$$

Note that 40 and 96 are the only multiples of 8 less than 100 that appear in the second row. Since Grandma Ana is less than 100 years old, we can conclude that last year she was 96 years old and Laura was 40. Therefore, Laura's current age is 41 years.