## PROBLEM 1

A three-digit number has its first two digits identical, and the third digit is 5. This number is divided by a one-digit number and the remainder is 8. Find the dividend, divisor, and quotient.
## Solution:

$$
\begin{aligned}
& \overline{a a 5}=b \cdot c+8,8<\mathrm{b}, \mathrm{b} \text { digit } \Rightarrow b=9 \text { (divisor)...................... } 2 \text{p}
\end{aligned}
$$

![](https://cdn.mathpix.com/cropped/2024_06_07_586ef55f110c0469ea02g-1.jpg?height=54&width=1122&top_left_y=960&top_left_x=263)

$$
\begin{aligned}
& \text { 110a=3(3c+1) ............................................................................... } 1 \text{p}
\end{aligned}
$$

![](https://cdn.mathpix.com/cropped/2024_06_07_586ef55f110c0469ea02g-1.jpg?height=63&width=1111&top_left_y=1058&top_left_x=260)

$$
\begin{aligned}
& \text { c = } 73 \text { (quotient)................................................................................1p } \\
& \overline{a a 5}=665 \text { (dividend) ...........................................................1p }
\end{aligned}
$$