Did not use

A father, mother, three children, both grandmothers, and both grandfathers were sitting at the table. Three of the family members used a knife and fork while eating. This is exactly half of those who used a fork and exactly three quarters of those who used a knife. No one ate with a spoon. How many family members did not use either a knife or a fork during dinner?

Final Answer:

x =  2

Step-by-step explanation:

$$\begin{gathered} n=1+1+3+2+2=9 \\ a+b+3+x=9 \\ 3=(a+3)/2 \\ 3=(b+3)\cdot 3/4 \\ a+b+x=6 \\ a=3 \\ 3b=3 \\ Row2-Row1\to Row2 \\ -b-x=-3 \\ Pivot:Row2\leftrightarrow Row3 \\ Row3-\frac{-1}{3}\cdot Row2\to Row3 \\ -x=-2 \\ x=\frac{-2}{-1}=2 \\ b=\frac{3}{3}=1 \\ a=6-b-x=6-1-2=3 \\ b=1 \\ x=2 \end{gathered}$$

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