Class children calculation

In the beginning, there are two boys and x girls. Then another three children will come to the class. In the end, there are three times fewer boys than girls. How many girls and boys are in the class

Final Answer:

c₁ =  2
d₁ =  6
c₂ =  3
d₂ =  9
c₃ =  4
d₃ =  12
c₄ =  4
d₄ =  15

Step-by-step explanation:

$$\begin{gathered} 3c=d \\ a+b=3 \\ c=a+2 \\ d=b+x \\ a{\ge }_0 \\ b{\ge }_0 \\ {a}_1=0,b_1=3,c_1=2,d_1=6,x_1=3 \\ {a}_2=1,b_2=2,c_2=3,d_2=9,x_2=7 \\ {a}_3=2,b_3=1,c_3=4,d_3=12,x_3=11 \\ {a}_4=3,b_4=0,c_4=5,d_4=15,x_4=15 \\ {c}_1=2 \end{gathered}$$

$d_1=6$

$c_2=3$

$d_2=9$

$c_3=4$

$d_3=12$

$c_4=4$

$d_4=15$

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