Solution Without Equations

The ratio of Eva's and Zdeněk's ages is currently 3:2; in six years this ratio will be 9:7.
a) How old are the siblings now?
b) By how many years and how many times older is Eva than Zdeněk?
c) By how many years and how many times older will Eva be than Zdeněk in twenty years?

This is seventh-grade material; we came up with a solution using equations, but my nephew hasn't covered those yet — is it possible to solve this without equations? Thank you.

Final Answer:

e =  12
z =  8
b₁ =  4
b₂ =  1.5
c₁ =  4
c₂ =  1.1429

Step-by-step explanation:

$$\begin{gathered} e:z=3:2 \\ (e+6):(z+6)=9:7 \\ e=3\cdot z/2 \\ (e+6)=9/7\cdot (z+6) \\ (3\cdot z/2+6)=9/7\cdot (z+6) \\ 3z=24 \\ z=\frac{24}{3}=8 \\ z=8 \\ e=3\cdot z/2=3\cdot 8/2=12 \end{gathered}$$

$b_1=e-z=12-8=4$

$b_2=e/z=12/8=\frac{3}{2}=1\frac{1}{2}=1.5$

$c_1=(e+20)-(z+20)=(12+20)-(8+20)=4$

$c_2=(e+20)/(z+20)=(12+20)/(8+20)=\frac{8}{7}=1\frac{1}{7}=1.1429$

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