I1.1 The equation $x^{2}-a x+(a+3)=0$ has equal roots. Find $a$, if $a$ is a positive integer.
11.2 In a test, there are 20 questions. $a$ marks will be given to a correct answer and 3 marks will be deducted for each wrong answer. A student has done all the 20 questions and scored 48 marks. Find $b$, the number of questions that he has answered correctly.

I1.3 If $x: y=2: 3, x: z=4: 5, y: z=b: c$, find $c$.
I1.4 Let $P(x, d)$ be a point on the straight line $x+y=22$ such that the slope of $O P$ equals to $c(O$ is the origin). Determine $d$.
$$
\begin{array}{l}
\Delta=(-a)^{2}-4(a+3)=0 \\
a^{2}-4 a-12=0 \\
(a-6)(a+2)=0 \\
a=6 \text { or } a=-2 \text { (rejected) }
\end{array}
$$

Reference: 1998 HG10
$$
\begin{array}{l}
6 b-3(20-b)=48 \\
9 b=108 \\
\Rightarrow b=12 \\
x: y: z=4: 6: 5 \\
y: z=6: 5=12: 10 \\
\Rightarrow c=10
\end{array}
$$

Reference: 1993 FI3.2
$$
\begin{array}{l}
x+d=22 \\
\Rightarrow x=22-d \\
m_{O P}=\frac{d}{x}=c \\
\Rightarrow \frac{d}{22-d}=10 \\
d=220-10 d \\
\Rightarrow d=20
\end{array}
$$