Statement 1

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10 years from now Toby will be twice as old

T + 10 = 2(...

as Julie was when (let P1 be the number of years ago)

T + 10 = 2(J-P1)

Melanie was 9 times as old as Toby.

M - P1 = 9(T - P1)

M - P1 = 9T - 9P1

8P1 = 9T - M

P1 = (9T - M)/8

Going back:

T + 10 = 2(J - [9T - M]/8)

8T + 80 = 16J - 18T + 2M

16J + 2M - 26T = 80

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8J + M - 13T = 40

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Statement 2

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Let the first "will be" be F1 years in the future.

Let the 2nd and 3rd "will be"s be F2 years in the future.

8 years ago, Melanie was half as old as Julie will be

2(M - 8) = J + F1,

when Julie is 1 year older than Toby will be...

J + F1 = 1 + (T + F2)

(First, get eqn. in terms of F1)

F1 = -J + T + F2 + 1

.... at the time when Melanie will be 5 times

as old as Toby will be 2 years from now.

M + F2 = 5(T + 2)

F2 = -M + 5T + 10

Substituting into expression for F1:

F1 = -J + T - M + 5T + 10 + 1

F1 = -J - M + 6T + 11

And, going back to the 1st eqn:

2(M - 8) = J - J - M + 6T + 11

2M - 16 = -M + 6T + 11

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3M - 6T = 27

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Statement 3

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When Toby was 1 year old,...

(T - 1 years ago)

Melanie was 3 years older than...

M - (T - 1) = 3 + ...

M - T + 1 = 3 + ....

...Toby will be when... (F3 years in the future)

M - T + 1 = 3 + (T + F3)

or,

F3 = M - 2T - 2

...Julie is 3 times as old as Melanie was 6 years before

J + F3 = 3(M - P2 - 6)

F3 = -J + 3M - 3P2 - 6

... the time (where "the time" is P2 years before now)

when Julie was half as old as Toby will be when ("when"

here is F4 years into the future)

J - P2 = 2(T + F4)

(get P2 on the left)

P2 = J - 2T - 2F4

...Melanie will be 10 years older than Melanie was

M + F4 = 10 + (M - P3)

F4 = 10 - P3

when Julie was one-third as old as Toby will be

J - P3 = 3(T + F5)

P3 = J - 3T - 3F5

when Melanie will be 3 times as old as she was when Julie was born.

M + F5 = 3(M - J)

F5 = 2M - 3J

Working backwards starting from four lines before:

P3 = J - 3T - 3F5 = J - 3T - 3(2M - 3J)

P3 = 10J - 6M - 3T

F4 = 10 - P3

F4 = -10J + 6M + 3T + 10

P2 = J - 2T -2F4

P2 = J - 2T + 20J - 12M - 6T - 20

P2 = 21J - 12M - 8T - 20

F3 = -J + 3M - 3P2 - 6

F3 = -J + 3M -63J + 36M + 24T + 60 - 6

F3 = -64J + 39M + 24T + 54

F3 = M - 2T - 2

-64J + 39M + 24T + 54 = M - 2T - 2

-64J + 38M + 26T = -56

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32J - 19M - 13T = -28

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So

8J + M - 13T = 40

3M - 6T = 27

32J - 19M - 13T = -28

Gives: J = 1/7 M = 25/7 T = -19/7

Clearly there are errors or misunderstandings or

most likely both.