Oranges

The mother divided her three children's oranges in a ratio of 6:5:4. Two children gave 45 oranges. How many oranges were there?

Correct answer:

n = 75

Step-by-step explanation:

a : b : c = 6 + 5 + 4 a + b = 45 ∣ ∣ b + c = 45 ∣ ∣ c + a = 45 k_{1} = \frac{6}{6 + 5 + 4} = \frac{2}{5} = 0.4 k_{2} = \frac{5}{6 + 5 + 4} = \frac{1}{3} ≐ 0.3333 k_{3} = \frac{4}{6 + 5 + 4} = \frac{4}{1 5} ≐ 0.2667 q_{1} = k_{1} + k_{2} = \frac{2}{5} + \frac{1}{3} = \frac{6}{1 5} + \frac{5}{1 5} = \frac{6 + 5}{1 5} = \frac{1 1}{1 5} ≐ 0.7333 q_{2} = k_{1} + k_{3} = \frac{2}{5} + \frac{4}{1 5} = \frac{6}{1 5} + \frac{4}{1 5} = \frac{6 + 4}{1 5} = \frac{1 0}{1 5} = \frac{2}{3} ≐ 0.6667 q_{3} = k_{3} + k_{2} = \frac{4}{1 5} + \frac{1}{3} = \frac{4}{1 5} + \frac{5}{1 5} = \frac{4 + 5}{1 5} = \frac{9}{1 5} = \frac{3}{5} = 0.6 n_{1} = 45 / q_{1} = 45 / \frac{1 1}{1 5} = 45 : \frac{1 1}{1 5} = 45 \cdot \frac{1 5}{1 1} = \frac{4 5 \cdot 1 5}{1 1} = \frac{6 7 5}{1 1} ≐ 61.3636 n_{2} = 45 / q_{2} = 45 / \frac{2}{3} = 45 : \frac{2}{3} = 45 \cdot \frac{3}{2} = \frac{4 5 \cdot 3}{2} = \frac{1 3 5}{2} = 67.5 n_{3} = 45 / q_{3} = 45 / \frac{3}{5} = 45 : \frac{3}{5} = 45 \cdot \frac{5}{3} = \frac{4 5 \cdot 5}{3} = \frac{2 2 5}{3} = 75 n = n_{3} = 75 a = k_{1} \cdot n = \frac{2}{5} \cdot 75 = \frac{2 \cdot 7 5}{5} = \frac{1 5 0}{5} = 30 b = k_{2} \cdot n = \frac{1}{3} \cdot 75 = \frac{1 \cdot 7 5}{3} = \frac{7 5}{3} = 25 c = k_{3} \cdot n = \frac{4}{1 5} \cdot 75 = \frac{4 \cdot 7 5}{1 5} = \frac{3 0 0}{1 5} = 20 n = 75

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