Family and age ratios

The age of father and son is in the ratio 10:3; the age of father and daughter is in the ratio 5:2. How old are father and son if the daughter is 20? In what ratio is the age of sister and brother?

Correct answer:

o =  50
s =  15
x =  4:3

Step-by-step explanation:

$$\begin{gathered} d=20 \\ 3o=10s \\ 2o=5d \\ 3o=10s \\ 2o=5\cdot 20 \\ 3\cdot o=10\cdot s \\ 2\cdot o=5\cdot 20 \\ 3o-10s=0 \\ 2o=100 \\ Row2-\frac{2}{3}\cdot Row1\to Row2 \\ 3o-10s=0 \\ 6.67s=100 \\ s=\frac{100}{6.66666667}=15 \\ o=\frac{0+10s}{3}=\frac{0+10\cdot 15}{3}=50 \\ o=50 \\ s=15 \end{gathered}$$

$x=d:s=20:15=4:3\approx 1.3333=4:3$

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