let

j = the age of Jetro

s = the age if Syenni

the ratio of the ages of Jetro and Syenni is 3:5

j : s = 3 : 5

5j = 3s

in 6 years time, the ratio of their ages will be 3:4

(j + 6) : (s + 6) = 3 : 4

4(j + 6) = 3(s + 6)

by solving the system of equations

5j = 3s

4(j + 6) = 3(s + 6)

we find

j = 6 years

s = 10 years

click here to see the step by step solution of the system of equations

Click to see all the steps

Syenni is 10 years old now.