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20 September, 12:05

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?

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  1. 20 September, 12:11
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    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.
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