João and Cláudia received their math test results back, but the digits of their scores were replaced by symbols. João's score was $\star$ and Cláudia's was $\star$ *. Together, they scored $* \square \boxplus$. Additionally, Cláudia scored 13 points more than João. What was each of their scores?
We need to find the values of the symbols in the sum

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-063.jpg?height=168&width=268&top_left_y=1832&top_left_x=928)

The two scores are two-digit numbers, and their sum has three digits, so the sum must be greater than 100 and less than 200. Therefore, we have $*=1$. However, Cláudia scored 13 points more than João, so,

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-063.jpg?height=165&width=211&top_left_y=2242&top_left_x=957)

Now, since the sum of $\star$ and 3 ends in 1, we have $\star=8$ and, therefore, $\square=6$. Thus, the scores of Cláudia and João are, respectively, 81 and 68.