Question 1107109
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G     = 8*C        (1)    ("A grandparent is eight times the age of a child.")

G + 1 = 7*(C+1)    (2)    ("One year from now the grandparent will be seven times the age the child will be then.")



From (1), substitute the expression of G into equation (2).  You will get


8C + 1 = 7*(C+1),


8C + 1 = 7C + 7  ====>  8C - 7C = 7 - 1  ====>  C = 6.


<U>Answer</U>.  The child is 6 years old.  The grandfather/grandmother is 6*8 = 48 years old.
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Solved.