In the fifth

In the fifth grade, which is attended by 88 pupils, two elective subjects are taught: mathematics exercises and sports games. 66 pupils did not attend mathematics exercises, which is 3 more than the number of pupils who did not sign up for sports games. 9 pupils signed up for both. a) How many pupils signed up for at least one elective subject? b) How many pupils signed up for exactly one elective subject?

Final Answer:

a =  38
b =  29

Step-by-step explanation:

$$\begin{gathered} m+s+9+x=88 \\ m+x=66-3 \\ s+x=66 \\ m+s+x=79 \\ m+x=63 \\ s+x=66 \\ Row2-Row1\to Row2 \\ -s=-16 \\ Row3+Row2\to Row3 \\ x=50 \\ s=\frac{-16}{-1}=16 \\ m=79-s-x=79-16-50=13 \\ m=13 \\ s=16 \\ a=m+s+9=13+16+9=38 \end{gathered}$$

$b=m+s=13+16=29$

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