Gustav’s father is seven times as old as he is. A year ago, he was nine times as old as Gustav. Find Gustav’s present age.
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To find Gustav's present age, let's assume that Gustav's age is 'x'.
According to the given information, Gustav’s father is seven times as old as Gustav, which means Gustav’s father’s age is 7x.
A year ago, Gustav was x-1 years old, and his father was 7x-1 years old.
The problem also states that a year ago, Gustav's father was nine times as old as Gustav. So we have the equation:
7x - 1 = 9(x - 1)
Now, let's solve this equation step by step:
7x - 1 = 9x - 9 [Expand the brackets]
-1 + 9 = 9x - 7x [Collect the like terms]
8 = 2x [Simplify]
4 = x [Divide both sides by 2]
Therefore, Gustav is presently 4 years old.