【Question 12】  
There are red and white balls in a box. The number of red balls is 4 times the number of white balls plus 3. Each time, 5 white balls and 17 red balls are taken out of the box. After several times, there are 4 white balls and 34 red balls left in the box. How many red balls were originally in the box? $\qquad$
【Analysis and Solution】
Profit and loss problem.
(Method One)
Let a total of $x$ times be taken; then there are $(5 x+4)$ white balls and $(17 x+34)$ red balls;
According to the problem, we get $4(5 x+4)+3=17 x+34$;
Solving for $x$ yields $x=5$;
The box originally had $17 \times 5+34=119$ red balls.
(Method Two)
If 5 white balls and 17 red balls are packed into one box, there will be 4 white balls and 34 red balls left; if 5 white balls and $5 \times 4=20$ red balls are packed into one box, there will be 4 white balls and $4 \times 4+3=19$ red balls left; there are $(34-19) \div(20-17)=5$ boxes;

The box originally had $17 \times 5+34=119$ or $20 \times 5=119$ red balls.