Together

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

Correct answer:

x₂ = 210

a : b : c = 6 : 5 : 4 a = 6 x b = 5 x c = 4 x a + b = 6 x + 5 x = 11 x = 126 (6 + 5) / 15 \cdot x_{1} = 126 11 x_{1} = 1890 x_{1} = \frac{1 8 9 0}{1 1} = 171.81818182 x_{1} = \frac{1 8 9 0}{1 1} ≐ 171.818182 b + c = 5 x + 4 x = 9 x = 126 (5 + 4) / 15 \cdot x_{2} = 126 9 x_{2} = 1890 x_{2} = \frac{1 8 9 0}{9} = 210 x_{2} = 210 a + c = 6 x + 4 x = 10 x = 126 (6 + 4) / 15 \cdot x_{3} = 126 10 x_{3} = 1890 x_{3} = \frac{1 8 9 0}{1 0} = 189 x_{3} = 189 Verifying Solution: a_{2} = \frac{6}{1 5} \cdot x_{2} = \frac{6}{1 5} \cdot 210 = \frac{6 \cdot 2 1 0}{1 5} = \frac{1 2 6 0}{1 5} = 84 b_{2} = \frac{5}{1 5} \cdot x_{2} = \frac{5}{1 5} \cdot 210 = \frac{5 \cdot 2 1 0}{1 5} = \frac{1 0 5 0}{1 5} = 70 c_{2} = \frac{4}{1 5} \cdot x_{2} = \frac{4}{1 5} \cdot 210 = \frac{4 \cdot 2 1 0}{1 5} = \frac{8 4 0}{1 5} = 56 s_{2} = b_{2} + c_{2} = 70 + 56 = 126 a_{3} = \frac{6}{1 5} \cdot x_{3} = \frac{6}{1 5} \cdot 189 = \frac{6 \cdot 1 8 9}{1 5} = \frac{1 1 3 4}{1 5} = \frac{3 7 8}{5} = 75 \frac{3}{5} = 75.6 b_{3} = \frac{5}{1 5} \cdot x_{3} = \frac{5}{1 5} \cdot 189 = \frac{5 \cdot 1 8 9}{1 5} = \frac{9 4 5}{1 5} = 63 c_{3} = \frac{4}{1 5} \cdot x_{3} = \frac{4}{1 5} \cdot 189 = \frac{4 \cdot 1 8 9}{1 5} = \frac{7 5 6}{1 5} = \frac{2 5 2}{5} = 50 \frac{2}{5} = 50.4 s_{3} = a_{3} + c_{3} = \frac{3 7 8}{5} + \frac{2 5 2}{5} = \frac{3 7 8 + 2 5 2}{5} = \frac{6 3 0}{5} = 126

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