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