Traja 33

Traja kamaráti si rozdelili guľôčky v pomere 6:5:4. Niektorí dvaja z nich dostali spolu 126 guľôčok. Koľko bolo spolu všetkých guľôčok?

Správna odpoveď:

x₂ =  210

Postup správneho riešenia:

$$\begin{gathered} a:b:c=6:5:4 \\ a=6x \\ b=5x \\ c=4x \\ a+b=6x+5x=11x=126 \\ (6+5)/15\cdot x_1=126 \\ 11x_1=1890 \\ {x}_1=\frac{1890}{11}=171,81818182 \\ {x}_1=\frac{1890}{11}\doteq 171,818182 \\ b+c=5x+4x=9x=126 \\ (5+4)/15\cdot x_2=126 \\ 9x_2=1890 \\ {x}_2=\frac{1890}{9}=210 \\ {x}_2=210 \\ a+c=6x+4x=10x=126 \\ (6+4)/15\cdot x_3=126 \\ 10x_3=1890 \\ {x}_3=\frac{1890}{10}=189 \\ {x}_3=189 \\ \text{ Skuˊsˇka spraˊvnosti: } \\ {a}_2=\frac{6}{15}\cdot x_2=\frac{6}{15}\cdot 210=\frac{6\cdot 210}{15}=\frac{1260}{15}=84 \\ {b}_2=\frac{5}{15}\cdot x_2=\frac{5}{15}\cdot 210=\frac{5\cdot 210}{15}=\frac{1050}{15}=70 \\ {c}_2=\frac{4}{15}\cdot x_2=\frac{4}{15}\cdot 210=\frac{4\cdot 210}{15}=\frac{840}{15}=56 \\ {s}_2=b_2+c_2=70+56=126 \\ {a}_3=\frac{6}{15}\cdot x_3=\frac{6}{15}\cdot 189=\frac{6\cdot 189}{15}=\frac{1134}{15}=\frac{378}{5}=75\frac{3}{5}=75,6 \\ {b}_3=\frac{5}{15}\cdot x_3=\frac{5}{15}\cdot 189=\frac{5\cdot 189}{15}=\frac{945}{15}=63 \\ {c}_3=\frac{4}{15}\cdot x_3=\frac{4}{15}\cdot 189=\frac{4\cdot 189}{15}=\frac{756}{15}=\frac{252}{5}=50\frac{2}{5}=50,4 \\ {s}_3=a_3+c_3=\frac{378}{5}+\frac{252}{5}=\frac{378+252}{5}=\frac{630}{5}=126 \end{gathered}$$

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