# Grandfather is #15# time the age of his grandson today, in #10# years the grandson will be #3/17# the age of the grandfather. How old are the grandfather and grandson?

Grandfather is

Grandson is

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Let's denote the current age of the grandson as ( G ) and the current age of the grandfather as ( G \times 15 ). In 10 years, the age of the grandson will be ( G + 10 ), and the age of the grandfather will be ( G \times 15 + 10 ).

According to the second statement, in 10 years, the age of the grandson will be ( \frac{3}{17} ) of the age of the grandfather:

[ G + 10 = \frac{3}{17} \times (G \times 15 + 10) ]

Expanding this equation:

[ 17(G + 10) = 3(G \times 15 + 10) ]

[ 17G + 170 = 45G + 30 ]

[ 170 - 30 = 45G - 17G ]

[ 140 = 28G ]

[ G = 5 ]

So, the grandson is currently 5 years old. The grandfather is ( G \times 15 = 5 \times 15 = 75 ) years old.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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