Birthdays 9011

Three sisters have birthdays today, and their ages are in the ratio of 2:3:4. In two years, their ages will be in the ratio of 5:7:9. Find what their ages will be in four years.

Correct answer:

p = 3:4:5

Step-by-step explanation:

a : b : c = 2 : 3 : 4 (a + 2) : (b + 2) : (c + 2) = 5 : 7 : 9 a = 2 \cdot x b = 3 \cdot x c = 4 \cdot x a + 2 = 5 \cdot y b + 2 = 7 \cdot y a - 2 x = 0 b - 3 x = 0 c - 4 x = 0 a - 5 y = - 2 b - 7 y = - 2 R o w 4 - R o w 1 \to R o w 4 a - 2 x = 0 b - 3 x = 0 c - 4 x = 0 2 x - 5 y = - 2 b - 7 y = - 2 R o w 5 - R o w 2 \to R o w 5 a - 2 x = 0 b - 3 x = 0 c - 4 x = 0 2 x - 5 y = - 2 3 x - 7 y = - 2 P i v o t : R o w 4 \leftrightarrow R o w 5 a - 2 x = 0 b - 3 x = 0 c - 4 x = 0 3 x - 7 y = - 2 2 x - 5 y = - 2 R o w 5 - \frac{2}{3} \cdot R o w 4 \to R o w 5 a - 2 x = 0 b - 3 x = 0 c - 4 x = 0 3 x - 7 y = - 2 - 0.33333 y = - 0.66667 y = \frac{- 0 . 6 6 6 6 6 6 6 7}{- 0 . 3 3 3 3 3 3 3 3} = 2 x = \frac{- 2 + 7 y}{3} = \frac{- 2 + 7 \cdot 2}{3} = 4 c = 0 + 4 x = 0 + 4 \cdot 4 = 16 b = 0 + 3 x = 0 + 3 \cdot 4 = 12 a = 0 + 2 x = 0 + 2 \cdot 4 = 8 a = 8 b = 12 c = 16 x = 4 y = 2 p = (a + 4) : (b + 4) : (c + 4) p = (8 + 4) : (12 + 4) : (16 + 4) p = 12 : 16 : 20 p = 3 : 4 : 5

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