>>Mrs.Carnie is three times as old as her daughter Sydney,<<
(1) M = 3S
>>...Sydney, who is twice as old as her brother, Cameron....<<
(2) S = 2C
>>If their total age is 63 years,...<<
(3) M + S + C = 63
Use (2) to substitute 2C for S in (1):
(1) M = 3S
M = 3(2C)
(4) M = 6C
Use (4) and (2) to substitute 6C for M and 2C for S in (3)
(3) M + S + C = 63
6C + 2C + C = 63
9C = 63
(5) C = 7
Use (5) to substitute 7 for C in (2)
(2) S = 2C
S = 2(7)
S = 14 <--- answer, Sydney's age.
------------------------------------------------
To check we find the mother's age by using (5) to substitute 7 for C in (4)
(4) M = 6C
M = 6(7)
M = 42
-----------------------------------------------
>>Mrs.Carnie is three times as old as her daughter Sydney,
The mother is 3 times Sydney's age 14, and 3x14 = 42. That checks.
>>Sydney, who is twice as old as her brother, Cameron.
That checks because Sydney is 14 and Cameron is 7. 14 is twice 7.
...If their total age is 63 years,
42 + 14 + 7 = 63. So it all checks.
Edwin