Today the ratio of Elinor's age to her mother's age is 3:8. After 15 years, the ratio will become 6:11. What is Elinor's age today?

X=Elinor's age today.

y=Mother's age today.

(x+15) = Elinor's age after 15 years.

(y+15) = Mohter's age after 15 years.

We can suggest this systemen of equations:

x/y=3/8 ⇒x=3y/8

(x+15) / (y+15) = 6/11 ⇒11 (x+15) = 6 (y+15)

Finally, we'll have the following system:

x=3y/8

11 (x+15) = 6 (y+15)

We can solve this system of equations by substitution method:

11[ (3y/8) + 15) = 6 (y+15)

11[ (3y+120) / 8) = 6y+90

33y+1320=8 (6y+90)

33y+1320=48y+720

33y-48y=720-1320

-15y=-600

y=-600/-15

y=40

We find out the value of "x";

x=3y/8

x=3 (40) / 8

x=120/8

x=15

Answer: Elinor is 15 years old.