Together

The three friends divided the balls in a ratio of 6: 5: 4. Some two of them got a total of 126 balls. How many balls were there together?

Correct answer:

x₂ =  210

Step-by-step explanation:

$$\begin{gathered} a:b:c=6:5:4 \\ a=6x \\ b=5x \\ c=4x \\ a+b=6x+5x=11x=126 \\ (6+5)\mathrm{/}15\cdot x_1=126 \\ 11x_1=1890 \\ {x}_1={\displaystyle \frac{1890}{11}}\doteq 171.818182 \\ b+c=5x+4x=9x=126 \\ (5+4)\mathrm{/}15\cdot x_2=126 \\ 9x_2=1890 \\ {x}_2=210 \\ a+c=6x+4x=10x=126 \\ (6+4)\mathrm{/}15\cdot x_3=126 \\ 10x_3=1890 \\ {x}_3=189 \\ \text{ Verifying Solution: } \\ {a}_2={\displaystyle \frac{6}{15}}\cdot x_2={\displaystyle \frac{6}{15}}\cdot 210=84 \\ {b}_2={\displaystyle \frac{5}{15}}\cdot x_2={\displaystyle \frac{5}{15}}\cdot 210=70 \\ {c}_2={\displaystyle \frac{4}{15}}\cdot x_2={\displaystyle \frac{4}{15}}\cdot 210=56 \\ {s}_2=b_2+c_2=70+56=126 \\ {a}_3={\displaystyle \frac{6}{15}}\cdot x_3={\displaystyle \frac{6}{15}}\cdot 189={\displaystyle \frac{378}{5}}=75\frac{3}{5}=75.6 \\ {b}_3={\displaystyle \frac{5}{15}}\cdot x_3={\displaystyle \frac{5}{15}}\cdot 189=63 \\ {c}_3={\displaystyle \frac{4}{15}}\cdot x_3={\displaystyle \frac{4}{15}}\cdot 189={\displaystyle \frac{252}{5}}=50\frac{2}{5}=50.4 \\ {s}_3=a_3+c_3=75.6+50.4=126 \end{gathered}$$

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