7. A, B, and C are playing a game. A thinks of a two-digit number, then multiplies this two-digit number by 100. B thinks of a number, then multiplies this one-digit number by 10. C thinks of a one-digit number, then multiplies this number by 7. Finally, the products of the three people are added together, and the result is 2024. Therefore, the sum of the numbers A, B, and C originally thought of is $(\quad)$ )
【Analysis】Number Theory, Place Value Principle 23
$$
\overline{a b} \times 100+10 c+7 d=2024 \text {, }
$$

Expand $1000 a+100 b+10 c+7 d=2024$, indeterminate equation, start with the largest coefficient, $a=2$ or $a=1$ $20+1+2=23,20+1+2=23$; cup =1, find no solution.