In prima, secunda and tertia

The numbers of children in prima, secunda and tertia are in the ratio 3 : 4 : 3. In prima and tertia together there are 12 more children than in secunda. How many children are in prima?

Final Answer:

a =  18

Step-by-step explanation:

$$\begin{gathered} a:b:c=3:4:3=3x:4x:3x \\ 3x=3x=>a=c \\ a+c=12+b \\ 3x+3x=12+4x \\ 3\cdot x+3\cdot x=12+4\cdot x \\ 2x=12 \\ x=\frac{12}{2}=6 \\ x=6 \\ a=3\cdot x=3\cdot 6=18 \\ b=4\cdot x=4\cdot 6=24 \\ c=3\cdot x=3\cdot 6=18 \end{gathered}$$

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